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.

A. and

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

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.

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.

Therefore, at t=5 we will get 5744.6.

We will see that the initial amount is A = 350, and the rate of growth is r = 75% per unit of time.

Finally, the function evaluated in t = 5 is equal to 5,744.6

A general exponential growth equation is written as:

f(t) = A*(1 + r)^t

Where:

A is the initial amount, such that:

f(0) = A.

r is the rate of growth, and t is the variable.

Here the given equation is:

y = 350*(1 + 0.75)^t

So we can see that the initial value is:

A = 350

And the rate is:

r = 0.75

But we want to write the rate in percent form, so we multiply it by 100%.

r = 0.75*100% = 75%.

Finally, we want to evaluate the function in t = 5, this gives:

y = 350*(1 + 0.75)^5 = 5,744.6

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step-by-step explanation: 2