Question

The amount of money Aria has in the bank after T years is determined by the equation A = 1,000 · 1.0512^T. After how many years will Aria have $2,000 in the bank?

(1) 12.9 (2) 13.9
(3) 14.9
(4) 15.9

Answer 1

Explanation:

You are given most of the equation that you need to solve. To find the number of years it will take to have 2000, sub in 2000 for A and solve:

`2000=1000(1.0512)^t` and begin by dividing away the 1000 on both sides to get

`2=(1.0512)^t` now we have to take the natural log of both sides:

`ln(2)=ln(1.0512)^t`. Taking the natural log allows us to bring the t down out front:

ln(2) = t ln(1.0512) and now divide both sides by ln(1.0512):

`(ln(2))/(ln(1.0512))=t` and do this on your calculator to get

t = 13.9 years

Answer 2

T = 13.9

Explanation:

A = 1,000 · 1.0512^T

Let A = 2000

2000 = 1,000 · 1.0512^T

Divide each side by 1000

2000/1000 = 1,000/1000 · 1.0512^T

2 = 1.0512^T

Take the log of each side

log 2 = log 1.0512^T

We know log a^b = b log a

log 2 = T log 1.0512

Divide each side by log 1.0512

log 2 / log 1.0512 = T

T=13.88172

Rounding to the nearest tenth

T = 13.9