1. **State the problem:** Find the approximate monthly percent change for the function $f(t) = 16(1.4)^t$ which models the number of deer after $t$ years.
2. **Recall the yearly growth rate:** The yearly growth rate is 40%, so the growth factor per year is $1 + 0.4 = 1.4$.
3. **Convert yearly growth to monthly growth:** Since there are 12 months in a year, the monthly growth factor $r$ satisfies:
$$ (1 + r)^{12} = 1.4 $$
4. **Solve for $r$:**
$$ 1 + r = \sqrt[12]{1.4} $$
5. **Calculate $r$ approximately:**
$$ r = \sqrt[12]{1.4} - 1 $$
Using a calculator,
$$ r \approx 1.0283 - 1 = 0.0283 $$
6. **Convert to percentage:**
$$ 0.0283 \times 100 = 2.83\% $$
7. **Interpretation:** The approximate monthly percent change is about 2.83%, not 0.03% as initially suggested.
**Final answer:** The monthly percent change is approximately **2.83%**.
Monthly Percent Change D60Af8
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