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!