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 $$y=·.

Answer 1

To model the population of the insects after \( x \) weeks with an initial population of 312 and a growth rate of 5% per week, you can use the exponential growth formula:

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

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

In this case:
- \( y_0 = 312 \)
- \( r = 0.05 \)

Plugging these values into the equation gives:

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

This simplifies to:

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

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

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