homework. 1. (7.3) what is natural base e? 1. answer euler’s number: 2.718281
TRANSCRIPT
![Page 1: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/1.jpg)
HOMEWORK
![Page 2: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/2.jpg)
1.(7.3)
What is Natural Base e?
![Page 3: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/3.jpg)
1. ANSWER
Euler’s Number: 2.718281
![Page 4: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/4.jpg)
2.(7.4 D1)
What is a common
logarithm?
![Page 5: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/5.jpg)
2 . ANSWER
A log with a base of 10.
Written as log.
![Page 6: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/6.jpg)
3.(7.4 D1)
What is a natural
logarithm?
![Page 7: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/7.jpg)
3 . ANSWER
A log with a base of e.Written as
ln.
![Page 8: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/8.jpg)
4. M(7.1 D3)
What is the formula for Compound Interest?
![Page 9: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/9.jpg)
4 . ANSWER
A = amount after t yearsP = initial Principal (deposit)
r = interest Ratet = time in years
n = times per year
![Page 10: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/10.jpg)
5. M(7.3)
What is the formula for Continuously
Compounded Interest?
![Page 11: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/11.jpg)
5 . ANSWER
![Page 12: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/12.jpg)
6. M(7.5)
What is the formula for the
Product Property?
![Page 13: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/13.jpg)
6 . ANSWER
![Page 14: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/14.jpg)
7. M(7.5)
What is the formula for
the Quotient Property?
![Page 15: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/15.jpg)
7 . ANSWER
![Page 16: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/16.jpg)
8. M(7.5)
What is the formula for the Power Property?
![Page 17: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/17.jpg)
8 . ANSWER
![Page 18: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/18.jpg)
9. M(7.5)
What is the formula for Change of
Base?
![Page 19: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/19.jpg)
9 . ANSWER
![Page 20: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/20.jpg)
10. M(7.)
What is the Exponential
Growth Model?
![Page 21: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/21.jpg)
10 . ANSWER
![Page 22: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/22.jpg)
11. M(7.)
What is the Exponential
Decay Model?
![Page 23: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/23.jpg)
11 . ANSWER
![Page 24: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/24.jpg)
12.
How do you know if an
exponential function is a
growth or decay function?
![Page 25: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/25.jpg)
12 . ANSWER
You look at b in the equation
If 0 <b < 1, it is a decay function.
If b > 1, it is a growth function.
![Page 26: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/26.jpg)
13. SOLVE(7.3)
You deposit $700 in an account that pays 3.5%
annual interest compounded
continuously. What is the balance after 2 years?
![Page 27: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/27.jpg)
13 . ANSWER
A = $750.76
![Page 28: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/28.jpg)
14. SOLVE(7.1-7.2)
How do you translate an exponential
function when graphing?
![Page 29: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/29.jpg)
14 . ANSWER
h = left & right (sign changes)k = up & down
![Page 30: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/30.jpg)
19. SOLVE(7.4 D2)
Simplify the expression
![Page 31: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/31.jpg)
15 . ANSWER
cancels out4x
![Page 32: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/32.jpg)
16. SOLVE(7.4)
Rewrite the expression
.
![Page 33: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/33.jpg)
16 . ANSWER
![Page 34: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/34.jpg)
17. SOLVE(7.4)
Find the inverse
function of .
![Page 35: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/35.jpg)
17 . ANSWER
Swap x & y.X – 2 =
cancels out
y=
![Page 36: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/36.jpg)
18. SOLVE(7.5)
Condense the expression:
y = 2log x + 3log y – 5log z
![Page 37: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/37.jpg)
18 . ANSWER
y = 2log x + 3log y – 5log z
Power Property:
Product Property
Quotient Property
![Page 38: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/38.jpg)
19. SOLVE(7.6)
Solve the equation:
![Page 39: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/39.jpg)
19 . ANSWER
Drop the
x – 7 = 2x + 3
Subtract x from both sides.
-7 = x + 3
Subtract 3 from both sides.
-10 = x
![Page 40: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/40.jpg)
20. SOLVE(7.6)
Solve the equation:
![Page 41: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/41.jpg)
20 . ANSWER
Cancels out.
X =
Change of Base
X = 2.07
![Page 42: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/42.jpg)
21. SOLVE(7.7)
Write an exponential function in the form
that passes through the points (3, 1) and (5, 4).
![Page 43: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/43.jpg)
21 . ANSWER
, (3, 1) and (5, 4).
2 = b
a = 1/8
![Page 44: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/44.jpg)
22. SOLVE(7.7)
Write a power function in the form that passes through the points (2, 3) and
(6, 12).
![Page 45: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/45.jpg)
22 . ANSWER
, (2, 3) and (6, 12)
12 = 3()
4 =
b =
b = 1.26
= 1.25
y = 1.25
![Page 46: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/46.jpg)
BONUS
Write an exponential growth function of the form whose graph has a y-intercept of 5 and
an asymptote of 2.
![Page 47: HOMEWORK. 1. (7.3) What is Natural Base e? 1. ANSWER Euler’s Number: 2.718281](https://reader035.vdocuments.us/reader035/viewer/2022062407/56649dd35503460f94acb320/html5/thumbnails/47.jpg)
BONUS
Explain how you can determine if a
power function is a good model for a set
of data pairs.