Question

i really need help guys!!

Answer 1

Since at t=0 (initial time) the population was 4000, we know that our base A=4000.
At t=8, P=4400. Since we already know A, we can substitute to solve for k like so
\[4400=4000e ^{8k}\]

Answer 2

Divide both sides of the equation to get
\[1.1=e ^{8k}\]

Answer 3

To eliminate e and solve for k, we can take the natural log of both sides of the equation to get
\[\ln 1.1=\ln e ^{8k}\]

Answer 4

Our equation should now be 8k=ln 1.1
Now just divide both sides by 8 to solve for k.
Your value for k should be k=.0119

Answer 5

Now that we have found our k value, we can find the population P at t=9.
We can set up our equation for P like so
\[P=4000e ^{.0119(9)}\]

Answer 6

If put into your calculator correctly, your answer to the question should be 4452.
Hope this helped! :)