Question

Math please help!!!!

Answer 1

Answer:

6.3 years

Step-by-step 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

$t = \frac{\log(0.4464)}{\log(0.88)}$

$t = \frac{-0.3503}{-0.0555}$

$t = 6.31$

$t \approx 6.3$