1. A savings account is started with an initial deposit of $500. The account earns 1.5% interest compounded annually.

(a) Write an equation to represent the amount of money in the account as a function of time in years.

(b) Find the amount of time it takes for the account balance to reach $800. Show your work.

thank you so much!

Guest Nov 6, 2018

#1**+2 **

We have the following "formula"

A = P ( 1 + r)^t

Where

A = 800

P = 500

r = 1.5% = .015

And we are looking for t

So we have

800 = 500 ( 1 + .015)^t divide both sides by 500

(800/500) = (1 + .015)^t

(8/5) = (1.015)^t take the log of both sides

log (8/5) =log (1.015)^t and we can write

log(8/5) = t * log (1.015) divide both sides by log(1.015)

log(8/5) /log (1.015) = t ≈ 31. 57 yrs = 32 years (to the nearest year)

CPhill
Nov 6, 2018