You deposit $500 in a savings account that earns 6% annual interest compounded yearly. Write and solve an exponential equation in terms of x to determine when the balance of the account will be $800. Round to the nearest hundredth.

Answer: x = 8.06 years

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P (1+r/n) ^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited.

t represents the number of years

From the information given,

P = 500

r = 6% = 6/100 = 0.06

n = 1 because it was compounded once in a year.

t = x

Therefore, the exponential equation in terms of x is

A = 500 (1 + 0.06/1) ^1 * x

A = 500 (1.06) ^x

If A = $800, then

800 = 500 (1.06) ^x

800/500 = 1.06) ^x

1.6 = 1.06) ^x

Taking log of both sides, it becomes

Log 1.6 = log 1.06^x = xlog1.06

0.204 = 0.0253 * x

x = 0.204/0.0253

x = 8.06