Agroup of entomologists has determined that the population of ladybugs at a local park can be modeled by the equation y = − 1.437 x + 197.686 , where x represents the number of years since 2010 and y represents the number of ladybugs, in thousands.
a) predict the ladybug population at the park in 2024.
b) predict the ladybug population at the park in 2060.

A) 177.568 thousand.

B) 125.836 thousand.

In this question, it is asking you to use the equation to find the population of ladybugs in a certain year.

Equation we're going to use:

We know that the "x" variable represents the number of years since 2010, so that means our starting year is 2010.

Lets solve the question.

Question A:

We need to find the ladybug population is 2024.

2024 is 14 years after 2010, so our "x" variable will be replaced with 14.

Your equation should look like this:

Now, we solve.

You should get 177.568

This means that the population of ladybugs in 2024 is 177.568 thousand.

Question B:

We need to find the ladybug population is 2060.

2060 is 50 years after 2010, so the "x" variable would be replaced with 50.

Your equation should look like this:

Now, we solve.

This means that the population of ladybugs in 2060 would be 125.836 thousand.

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