Question

Identify the initial amount a and the rate of growth r (as a percent) of the exponential function y=350(1+0.75)t. Evaluate the function when t=5. Round your answer to the nearest tenth.

Answer 1

Answer:

A. $a=350$ and $r=75\%$

B. 5744.6.

Step-by-step explanation:

We have been given an exponential function $y=350(1+0.75)^t$ 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: $y=a*b^x$, 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 $y=a*(1+r)^x$

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.

$r=0.75*100=75\%$

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.

$y=350(1+0.75)^5$

$y=350(1.75)^5$

$y=350*16.4130859375$

$y=5744.580078125\approx 5744.6$

Therefore, at t=5 we will get 5744.6.