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=2.294e−0.654t 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?