Question

Rewrite y = 2(10)t/12 in the form y = a(1+r)t or y = a(1 - r). Round the value of r to

the nearest ten thousandth. Then tell whether the model represents exponential growth or
exponential decay.​

Answer 1

• 
  `y=2(1+0.2115)^t`
• Exponential growth.

Explanation:

Given that:
`y=2(10)^(t/12)`

To rewrite the model in the form
`y = a(1+r)^t` or
`y = a(1 - r)^t`

`y=2(10)^{(t)/(12) }\\=2[(10)^(1)/(12)]^(t)\\=2[1.2115]^t\\`

`y=2(1+0.2115)^t` is in the form
`y = a(1+r)^t` or
`y = a(1 - r)^t` where r=0.2115.

Since 1.2115>1, the model represents an exponential growth.