A population of a Jellybean is growing exponentially. At the given timet, in years, the population J(t) is given by J(t) = J(0)ekt, where k is a con-stant.
(a) If the population was 200 in 2007 and 450 in 2012, find k.
(b) What is the expected population for 2020?
(c) In what year would you expect the population of Jellybeans to reach one million?

Originally Posted by mathkid182
A population of a Jellybean is growing exponentially. At the given timet, in years, the population J(t) is given by J(t) = J(0)ekt, where k is a con-stant.
(a) If the population was 200 in 2007 and 450 in 2012, find k.
(b) What is the expected population for 2020?
(c) In what year would you expect the population of Jellybeans to reach one million?
Here are some hints.

a) $\displaystyle J(2007)=200=J_0(e^{2007k})$ and $\displaystyle J(2012)=450=J_0(e^{2012k})$.

Dividing the two equations gives $\displaystyle \frac{200}{450}=e^{2007k-2012k}=e^{5k}$. Use this to solve for $\displaystyle k$. Having solved for $\displaystyle k$, use either one of the original equations I gave you to solve for $\displaystyle J_0$

b) Now that you have values for $\displaystyle J_0$ and $\displaystyle k$, simply calculate $\displaystyle J(2020)$

c) Solve the equation $\displaystyle J(t)=J_0e^{kt}=1,000,000$ for $\displaystyle t$.