Subjects algebra

Monthly Percent Change D60Af8

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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%**.