6.1E: Exponential Functions (Exercises)

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Dec 26, 2024
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- 6.1: Exponential Functions
- 6.2: Graphs of Exponential Functions

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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.

Table 1
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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