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)

Question

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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:

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