Question

Please help. I'm so confused

Answer 1

We can solve for the year when the population of California, A, reached 40 million by setting A equal to 40 and solving for t:

A = 37.3e^(0.0095t)

40 = 37.3e^(0.0095t)

Divide both sides by 37.3:

40/37.3 = e^(0.0095t)

Take the natural logarithm of both sides:

ln(40/37.3) = 0.0095t

Divide both sides by 0.0095:

t = ln(40/37.3)/0.0095

Using a calculator, we get:

t ≈ 6.24

Therefore, the population of California reached 40 million about 6.24 years after 2010. To find the exact year, we add 6.24 years to 2010:

2010 + 6.24 ≈ 2016.24

So the population of California reached 40 million around the year 2016.24, or about the middle of 2016

Hope this helps!