Question

3. 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. Answer:

Answer 1

Answer:

31.334... years

Step-by-step explanation:

Initial value = $500

r = 1.5%

t = ?

A = (500)$e^{.015*t}$

I was unsure if the question was asking to express the equations in terms of t =, but i did those steps anyway just in case.

A/500 = $e^{.015*t}$

ln A/500 = ln$e^{.015*t}$

ln A/500 = .015*t

ln(A/500)/.015 = t

t = ln(A/500)/.015

To find the amount of time it takes for the account balance to reach $800, we plug in $800 for A in the equation that solves for t.

t= ln(800/500)/.015 = 31.334...(rounded) years

We also could have solved by plugging in $800 into the original equation and then solving for t, but i found it to be easier to find the equation for t prior to solving. Hope this helps!