Please help! The problem is in the picture:

Answers:

Note: your teacher may want you to type in a positive value for r

Explanation:

The given equation y = 8(1-0.15)^t is in the form y = a(1+r)^t

We have a = 8 as the initial value, or what we start with.

r = -0.15 converts to -15%, so we have a decay of 15%

Plug in t = 3 to find the corresponding value of y

y = 8(1-0.15)^t

y = 8(1-0.15)^3

y = 8(0.85)^3

y = 8(0.614125)

y = 4.913

y = 4.9

a = 8

r = 85%

y = 4.913

Step-by-step explanation:

For a, the exponential decay function is y=a*r^t. In order to find the initial amount, you are solving for when t = 0 or, y(0). Thus, t, or time, is 0. Solve the equation with time of 0.

y = 8(1-0.15)^0 = 8*1 (anything to the 0 power equals 1)

a = 8 is the initial amount

In order to solve for r, you need to solve (1 - 0.15) = 0.85. Now, multiply by 100 to get the percent 100 * 0.85 = 85%

Lastly, when t = 3 solve the equation filling in the exponent, t with 3 like below:

y = 8(1-0.15)^3 (PEMDAS; parenthesis and exponents first)

y = 8(0.85)^3 = 8*(0.614125)

y = 4.913

17.08

correct me if i am wrong.