A ship embarked on a long voyage. At the start of the voyage, there were 300 ants in the cargo hold of the ship. One week into the voyage, there were 600 ants. Suppose the population of ants is an exponential function of time. There also was an exponentially-growing population of anteaters on board. At the start of the voyage there were 19 anteaters, and the population of anteaters doubled every 2.4 weeks. How long into the voyage were there 200 ants per anteater?
So I got the exponential equation for ants to be $y=300(2^{x\text{ weeks}})$. So for the anteaters I got $y=19(2^{x/2.4})$. So if I set the $2$ equations equal to each other and solve I get $0.416666667$ and every other way I try to do this problem I get confused and get weird numbers. The sample prob is: ants $= 500 (1.6^x)$ and anteaters $= 18(2^{x.2.8})$ and the answer was $8.617$ weeks
Hint: Your equations for ants and anteaters are correct, but you should not use the same variable on the left. Let $y$ be the number of ants at time $x$ (measured in weeks), then you are right that $y=300 \cdot 2^x$ and if $z$ is the number of anteaters you have $z=19 \cdot 2^{x/2.4}$. Now you are asked for the time when $y=200z$, so set those equal.