# 6.1E: Exponential Functions (Exercises)

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1. Determine whether the function $$y=156(0.825)^{t}$$ represents exponential growth, exponential decay, or neither. Explain

2. The population of a herd of deer is represented by the function $$A(t)=205(1.13)^{t},$$ where $$t$$ is given in years. To the nearest whole number, what will the herd population be after 6 years?

3. Find an exponential equation that passes through the points (2,2.25) and (5,60.75) .

4. Determine whether Table 1 could represent a function that is linear, exponential, or neither. If it appears to be exponential, find a function that passes through the points.

 x 1 2 3 4 f(x) 3 0.9 0.27 0.081

5. A retirement account is opened with an initial deposit of $$\ 8,500$$ and earns $$8.12 \%$$ interest compounded monthly. What will the account be worth in 20 years?

6. Hsu-Mei wants to save $$\ 5,000$$ for a down payment on a car. To the nearest dollar, how much will she need to invest in an account now with $$7.5 \%$$ APR, compounded daily, in order to reach her goal in 3 years?

7. Does the equation $$y=2.294 e^{-0.654 t}$$ represent continuous growth, continuous decay, or neither? Explain.

8. Suppose an investment account is opened with an initial deposit of $$\ 10,500$$ earning $$6.25 \%$$ interest, compounded continuously. How much will the account be worth after 25 years?

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