Exponential Functions, Growth, and Decay (2 Questions)

• Tell whether each function represents growth or decay, then graph by using a table of values:

• 1. 0.5(1.25)x

Inverses (3 questions)

• Write the inverse of the following function:

• 2.

y 3x 7

10

Logarithmic functions (4 questions)

• Write the exponential in logarithmic form:• 3. 35 =343

• Write the logarithmic in exponential form:• 4. 2 = logo.6 0.36

Properties of logarithms (6 questions)

• Express as a single logarithm and simplify• 5. log2 8+ log2 16

• 6. log 10 – log 0.1

• 7. ln e4x 8. e4 ln x

• 9. log 1064 – 2(10log 16)log2 16

Exponential and Logarithmic Equations (4 questions)

• Solve:• 10. 3x-1 = 1/9 11. 5x =

50

• 12. 2x+4 = 20

• 13. log (x – 2) + log (x + 2) = 21

The natural Base, e (4 questions, overlapping with properties of logs)

• Simplify:• 14. eln(2x+1) 15. ln e14x

• 16. Use the natural decay function: N(t) = N0e-kt to find the age of a fossil

containing 30% of the original amount of a substance whose half life is 5000 years.

Transformations (2 questions)

• 17. Write the transformed function: f(x) = log (x – 1) is translated

5 units right at then reflected across the x-axis.

18.Write the transformed function:f(x) = ex is reflected across the x –

axis, stretched vertically by a factor of 3, and shifted 2 units down.

Exponential and Logarithmic Regressions (2 questions)

• The table gives the population size of a flock of birds in one habitat over the last 55 years.

• Find an exponential regression for the data.

Years since Data was first collected

Population Size

5 18

22 22

40 85

57 185