Answer:
A.
and ![r=75\%](https://tex.z-dn.net/?f=r%3D75%5C%25)
B. 5744.6.
Step-by-step explanation:
We have been given an exponential function
and we are asked to identify the initial amount and the rate of growth of our given function.
A. Since we know that an exponential function is in form:
, where,
a = Initial value,
b = For growth b is in form (1+r), where r is in decimal form.
So, the exponential growth function is ![y=a*(1+r)^x](https://tex.z-dn.net/?f=y%3Da%2A%281%2Br%29%5Ex)
Upon comparing the given exponential function with our exponential function we can see that a equals 350 and r equals 0.75.
Since growth rate is given in decimal form, so let us convert it as percent by multiplying by 100.
![r=0.75*100=75\%](https://tex.z-dn.net/?f=r%3D0.75%2A100%3D75%5C%25)
Therefore, initial amount a is 350 and rate of growth is 75% for our given function.
B. Let us evaluate our function at t=5 by substituting t=5 in our given function.
![y=350(1+0.75)^5](https://tex.z-dn.net/?f=y%3D350%281%2B0.75%29%5E5)
![y=350(1.75)^5](https://tex.z-dn.net/?f=y%3D350%281.75%29%5E5)
![y=350*16.4130859375](https://tex.z-dn.net/?f=y%3D350%2A16.4130859375)
![y=5744.580078125\approx 5744.6](https://tex.z-dn.net/?f=y%3D5744.580078125%5Capprox%205744.6)
Therefore, at t=5 we will get 5744.6.