the formula A=19.6 e ^ 0.0138t models population of US state, A, in millions, t years after 2000. what was the population of state in 2000?

Question

b. when will the population of state reach 25.9 million?

Answer 1

The population is years measured after 2000 so 2000 is 0. Any number to the 0 power is 1 so the population is 19.6 (million).

For the second part, we need to know when it reaches 25.9 so 25.9=19.6e^0.0138t. Divide both sides by 19.6 and you get 1.32=e^0.01438t. Taking the natural log of both sides gives ln 1.32=0.0138t. That means it will be 25.9 million t=(ln 1.32)/0.138 years after. This works out to be 20.1 years after.

Answer 2

At t = 0 A = 19.6

25.9 = 19.6e^0.0138t

1.321428571 ≈ e^0.0138t

ln 1.321428571 ≈ 0.0138t

Can you solve for t and answer?