Answer:28.8
Step-by-step explanation:
It looks like the given equation says
![xy^8 + e^{y/5} = e](https://tex.z-dn.net/?f=xy%5E8%20%2B%20e%5E%7By%2F5%7D%20%3D%20e)
When <em>x</em> = 0, you have
![0\cdot y^8 + e^{y/5} = e \\\\ e^{y/5} = e^1 \\\\ \dfrac y5 = 1 \\\\ y=5](https://tex.z-dn.net/?f=0%5Ccdot%20y%5E8%20%2B%20e%5E%7By%2F5%7D%20%3D%20e%20%5C%5C%5C%5C%20e%5E%7By%2F5%7D%20%3D%20e%5E1%20%5C%5C%5C%5C%20%5Cdfrac%20y5%20%3D%201%20%5C%5C%5C%5C%20y%3D5)
Differentiating both sides with respect to <em>x</em> gives
![\left(xy^8 + e^{y/5}\right)' = e' \\\\ \left(xy^8\right)' + \left(e^{y/5}\right)' = 0 \\\\ x\left(y^8\right)' + x'y^8 + e^{y/5}\left(\dfrac y5\right)' = 0 \\\\ 8xy^7y' + y^8 + \dfrac15e^{y/5}y' = 0](https://tex.z-dn.net/?f=%5Cleft%28xy%5E8%20%2B%20e%5E%7By%2F5%7D%5Cright%29%27%20%3D%20e%27%20%5C%5C%5C%5C%20%5Cleft%28xy%5E8%5Cright%29%27%20%2B%20%5Cleft%28e%5E%7By%2F5%7D%5Cright%29%27%20%3D%200%20%5C%5C%5C%5C%20x%5Cleft%28y%5E8%5Cright%29%27%20%2B%20x%27y%5E8%20%2B%20e%5E%7By%2F5%7D%5Cleft%28%5Cdfrac%20y5%5Cright%29%27%20%3D%200%20%5C%5C%5C%5C%208xy%5E7y%27%20%2B%20y%5E8%20%2B%20%5Cdfrac15e%5E%7By%2F5%7Dy%27%20%3D%200)
That is, the derivative operator distributes over sums, and the derivative of a constant is 0; apply the product rule on the first term and chain rule on the second; then use chain rule one more time.
Now plug in <em>x</em> = 0 and <em>y</em> = 5, and solve for <em>y'</em> :
![8\cdot0\cdot5^7y' + 5^8 + \dfrac15e^{5/5}y' = 0 \\\\ 5^8 + \dfrac15e y' = 0 \\\\ \dfrac15e y' = -5^8 \\\\ y' = \boxed{-\dfrac{5^9}e}](https://tex.z-dn.net/?f=8%5Ccdot0%5Ccdot5%5E7y%27%20%2B%205%5E8%20%2B%20%5Cdfrac15e%5E%7B5%2F5%7Dy%27%20%3D%200%20%5C%5C%5C%5C%205%5E8%20%2B%20%5Cdfrac15e%20y%27%20%3D%200%20%5C%5C%5C%5C%20%5Cdfrac15e%20y%27%20%3D%20-5%5E8%20%5C%5C%5C%5C%20y%27%20%3D%20%5Cboxed%7B-%5Cdfrac%7B5%5E9%7De%7D)
$12,838
7900/8= 987.5
For every one year, you invest $987.5
987.5 times 5 for 5 years= 4,937.5
If you round to the nearest dollar, it would be: $4,938
The total amount of money that would be in the account is, $12,838.
The answer would be 15,120