QuestionDecember 17, 2025

15. y=3220(1.0375)^x represents the population "y"of Stream City "X"years after 1910. Between which two years did the population surpass 15,000? (You may use a graph or a table.)

15. y=3220(1.0375)^x represents the population "y"of Stream City "X"years after 1910. Between which two years did the population surpass 15,000? (You may use a graph or a table.)
15. y=3220(1.0375)^x represents the population "y"of Stream City "X"years after 1910. Between which two years did the population surpass 15,000? (You may use a graph or a table.)

Solution
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Answer

Between 1951 and 1952 Explanation 1. Set up the equation for population surpassing 15,000 Solve 3220(1.0375)^x = 15000 for x. 2. Isolate x using logarithms x = \frac{\ln(15000/3220)}{\ln(1.0375)} 3. Calculate x x = \frac{\ln(4.658)}{\ln(1.0375)} \approx \frac{1.539}{0.0368} \approx 41.8 4. Find the years 1910 + 41 = 1951, 1910 + 42 = 1952

Explanation

1. Set up the equation for population surpassing 15,000<br /> Solve $3220(1.0375)^x = 15000$ for $x$.<br />2. Isolate $x$ using logarithms<br /> $x = \frac{\ln(15000/3220)}{\ln(1.0375)}$<br />3. Calculate $x$<br /> $x = \frac{\ln(4.658)}{\ln(1.0375)} \approx \frac{1.539}{0.0368} \approx 41.8$<br />4. Find the years<br /> $1910 + 41 = 1951$, $1910 + 42 = 1952$
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