When Interest Is Compounded Continuously, the Rate of Change of the Amount

Multiple Choice

When interest is compounded continuously, the rate of change of the amount x of the investment is proportional to the amount present. In this case, the proportionality constant is the annual interest rate r (as a decimal) ; that is, . If $2,500 is invested at 7%, compounded continuously, what will be the future value of this investment after 12 years? Round to the nearest cent. ​

A) $4,600.00
B) $5,776.80
C) $5,630.48
D) $5,708.32
E) $5,790.92