Chapter 3 Review PRECALCULUS

Describe how to transform the following graphs of 𝒇 into the graphs of 𝒈.

1. 𝑓(𝑥) = 𝑒 , 𝑔(𝑥) = 3𝑒 − 1

Find the y-intercept and asymptotes of the logistic equation.

2. 𝑓(𝑥) =∙

Tell whether the function is an exponential growth function or exponential decay function, and find the constant percentage rate of growth or decay.

3. 𝑃(𝑡) = 3.5 ∙ 1.09

Determine the exponential function that satisfies the given conditions.

4. Initial value = 5, increasing at a rate of 17% per year

5. Initial mass = 592 g, halving once every 6 months

Exponential Growth: The population of Smallville in the year 1890 was 6250. Assume the population increased at a rate of 2.75% per year.

6. Estimate the population in 1915 and 1940.

7. Predict when the population reached 50,000. Evaluate the logarithmic expression.

8. log 4 9. log 10 Solve the equations by changing them to exponential form.

10. log 𝑥 = 4

Chapter 3 Review PRECALCULUS Describe how to transform the graph of 𝒚 = 𝐥𝐨𝐠 𝒙 into the graph of the given function.

11. −3 log(1 − 𝑥) + 1 Use properties of logarithms to write the expression as a sum or difference of logarithms or multiple logarithms.

12. log 𝑥 𝑦 13. log

Assuming 𝒙, 𝒚, and 𝒛 are positive, use properties of logarithms to write the expression as a single logarithm.

14. log 𝑥 + log 𝑦 15. 4 log(𝑥𝑦) − 3 log(𝑦𝑧)

Use the change-of-base formula and your calculator to evaluate the logarithm.

16. log 19

Find the exact solution algebraically.

17. 36⁄

= 4

18. 2 10 ⁄ = 20

19. log (1 − 𝑥) = 1

20. 50𝑒 . = 200

Determine how many orders of magnitude that quantities differ.

21. A $100 bill and a dime 22. A canary weighing 20 g and a hen weighing 2 kg

Find the amount accumulated via simple interest and via compound interest.

23. 𝑃 = $1500, 𝑟 = 7%, 𝑡 = 6

Chapter 3 Review PRECALCULUS Find the amount accumulated via compound interest.

24. 𝑃 = $1500, 𝑟 = 7%, 𝑡 = 5, 𝑘 = 4 Find the amount accumulated via continuously compounded interest.

25. 𝑃 = $1250, 𝑟 = 5.4%, 𝑡 = 6 Find the future value accumulated in an annuity …

26. 𝑅 = $500, 𝑟 = 7%, 𝑡 = 6, 𝑘 = 4 Find the present value of a loan…

27. 𝑟 = 4.7%, 𝑅 = $815.37, 𝑡 = 5

Equations…

Simple Interest 𝐴 = 𝑃(1 + 𝑟𝑡)

Compound Interest 𝐴 = 𝑃(1 + 𝑟)

Continuously Compounded Interest 𝐴 = 𝑃𝑒

Future Value

𝐹𝑉 = ( )

Present Value

𝑃𝑉 = ( )