Question

Math please help!!!!

Answer 1

6.3 years

Explanation:

Given

`P = 22400` --- initial value

`r = 12\%` -- rate

`A = P(0.88)^t` --- function

Required

Find t when
`A = 10000`

We have:
`A = P(0.88)^t`

Substitute:
`A = 10000` and
`P = 22400`

`10000 = 22400 * 0.88^t`

Divide both sides by 22400

`0.4464 = 0.88^t`

Take log of both sides

`\log(0.4464) = \log(0.88^t)`

Apply law of logarithm

`\log(0.4464) = t\log(0.88)`

Solve for t

`t = (\log(0.4464))/(\log(0.88))`

`t = (-0.3503)/(-0.0555)`

`t = 6.31`

`t \approx 6.3`