6.1E: Exponential Functions (Exercises)
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?