One year ago, Grace put $200 she earned from tutoring into an investment account. Today, the account's value has increased to $212, and it is expected to continue growing each year.
Write an exponential equation in the form y=a(b)x that can model the value of the investment account, y, x years after Grace started the account.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
To the nearest dollar, what can Grace expect the value of the account to be 6 years after starting the account if she makes no other deposits or withdrawals?
$
To model the value of the investment account, we can use the exponential equation:
y = 200(1.06)^x
where:
- a = 200 (initial investment amount)
- b = 1.06 (growth rate)
Therefore, the equation is y = 200(1.06)^x.
To calculate the value of the account 6 years after starting it, we replace x with 6 in the equation:
y = 200(1.06)^6
y = 200(1.418519)
y ≈ 283
Therefore, Grace can expect the value of the account to be around $283 6 years after starting it if she makes no other deposits or withdrawals.