Question

A group 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.

Answer 1

A) 177.568 thousand.

B) 125.836 thousand.

Explanation:

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:

`y = -1.437 x + 197.686`

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:

`y = -1.437 (14) + 197.686`

Now, we solve.

`y = -1.437 (14) + 197.686\\\\\text{Multiply -1.437 and 14}\\\\y=-20.118+197.686\\\\\text{Add}\\\\y=177.568`

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:

`y = -1.437 (50) + 197.686`

Now, we solve.

`y = -1.437 (50) + 197.686\\\\\text{Multiply -1.437 and 50}\\\\y=-71.85+197.686\\\\\text{Add}\\\\y=125.836`

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

I hope this helped you out.

Good luck on your academics.

Have a fantastic day!