Question

Success Criteria: 1. Determine the initial amount (a) ate 2. Determine the r given the (b), a. If the b is greater than 1 the function is growing so subtract 1 and convert remaining value to a percentage, b. If the b is less than 1, the function is decaying so subtract that value from 1 and convert the result to a percentage. 3. Determine the b given ther. a. If growth, then use b=1 + r. b. If decay, then use b= 1 - r. 4. Select the answer that matches the answers in 1 and 2 above.

Answer 1

`y\text{ = }13(0.8)^t\text{ (option }D)`

Step-by-step explanation:

Exponetial formula:

`\begin{gathered} f(x)=ab^x \\ a\text{ = initial amount} \\ x\text{ = time } \\ b\text{ = growth or decay factor} \end{gathered}`

a = initial value = 13

rate = r = 20% = 0.2

b = 1 + r

if b > 1 (if it is exponential growth)

if b< 1 (if it is decay)

b = 1 - r

we are told it decays:

b = 1- r

b = 1 - 0.2

b = 0.8

The exponential function becomes:

`\begin{gathered} y=f(t)=a(1-r)^t \\ y=13(1-0.2)^t \\ y\text{ = }13(0.8)^t\text{ (option }D) \end{gathered}`