Question

Julian opened a college savings account. The amount of money in his account can be calculated using the function c(t) = 600(1.02)t, where t represents the time in years since the initial deposit. What does the value 600 represent in the function?

1) The amount of interest Julian will earn each year
2) The amount of money for Julian's initial deposit
3) The amount of money in Julian's account after one year
4) The maximum amount of money Julian can earn in his account

Answer 1

In the function c(t) = 600(1.02)t, the value 600 represents Julian's initial deposit into his college savings account. This amount is the principal that will accumulate interest over time.

Step-by-step explanation:

The function c(t) = 600(1.02)t represents the amount of money in Julian’s college savings account over time, where t represents time in years. In this function, 600 represents the initial amount of money, or the principal, that Julian deposited into the account. This is a classic example of a compound interest formula where the initial deposit is multiplied by (1 + rate of interest) raised to the number of times interest is applied.

So, the value 600 in the function is Julian’s initial deposit. It is not the amount of interest Julian earns each year, the amount after one year, or the maximum amount of money he can earn, as those figures will change depending on the time t and the interest being compounded annually.