To create an exponential function to represent a population of insects growing at a rate of 7%, we use the general formula for exponential growth, which is:
\[ f(x) = P_0 \cdot (1 + r)^x \]
where:
- \( P_0 \) is the initial population,
- \( r \) is the growth rate (as a decimal),
- \( x \) is the time (in whatever units you're measuring).
In this case:
- The initial population \( P_0 \) is 50,
- The growth rate \( r \) is 7%, which is 0.07 when converted to decimal.
Substituting these values into the formula gives us:
\[ f(x) = 50 \cdot (1 + 0.07)^x \] \[ f(x) = 50 \cdot (1.07)^x \]
So, the correct option is:
f(x) = 50(1.07)^x.
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