To represent a population that is growing exponentially, you can use the standard formula:
\[ P(t) = P_0 \cdot (1 + r)^t \]
where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population,
- \( r \) is the growth rate (expressed as a decimal),
- \( t \) is the time in appropriate units (for example, days, months, etc.).
In this case:
- The initial population, \( P_0 \), is 50 insects.
- The growth rate, \( r \), is 7%, which is 0.07 in decimal form.
Substituting the values into the formula gives:
\[ P(t) = 50 \cdot (1 + 0.07)^t \] \[ P(t) = 50 \cdot (1.07)^t \]
Thus, the correct function representing the population of 50 insects growing at a rate of 7% is:
f(x) = 50(1.07)^x
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