Question

Shiloh opens a savings account in which interest is compounded annually. The balance in the account is given by the following exponential expression, where t represents the time in years.

125(1.025)^t
Which statement correctly interprets the given expression?
A. Shiloh initially invested $125, which grows annually at a rate of 1.025%.
B. Shiloh initially invested $125, which grows annually at a rate of 2.5%.
C. Shiloh initially invested $1,025, which grows annually at a rate of 1.25%.
D. Shiloh initially invested $1,025, which grows annually at a rate of 12.5%.

Answer 1

B. Shiloh initially invested $125, which grows annually at a rate of 2.5%.

Explanation:

We have been given that Shiloh opens a savings account in which interest is compounded annually. The balance in the account is given by the exponential expression
`125(1.025)^t` , where t represents the time in years.

Since we know that an exponential function is in form
`y=a\cdot (b)^x` and for growth b=1+r.

a= initial value, r= rate in decimal form.

Upon comparing our given function with exponential function we can see that initial amount is 125.

As rate of an exponential function is in decimal form, therefore, 0.025 equals 0.025*100=2.5%.

Upon looking at our given options we can see that option B is the correct choice as Shiloh initially invested $125, which grows annually at a rate of 2.5%.