Question

The population of certain insects is initially 312. The insect population shows exponential growth of 5% each week. Write the exponential equation to model the insect population, y, after x weeks.(1 point)
The equation is $$
.

Answer 1

The exponential growth of the insect population can be modeled by the equation:

\[
y = y_0 \cdot (1 + r)^x
\]

where:
- \(y\) is the population after \(x\) weeks,
- \(y_0\) is the initial population,
- \(r\) is the growth rate (as a decimal),
- \(x\) is the number of weeks.

In this case:
- The initial population \(y_0 = 312\),
- The growth rate \(r = 0.05\) (which is 5% expressed as a decimal).

Substituting these values into the equation gives:

\[
y = 312 \cdot (1 + 0.05)^x
\]

So, the exponential equation to model the insect population after \(x\) weeks is:

\[
y = 312 \cdot (1.05)^x
\]