Solve.
-The value of a particular investment follows a pattern of exponential growth. In the year 2000 , you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential growth model $\mathrm { A } = 1700 \mathrm { e } ^ { 0.062 \mathrm { t } }$. When will the account be worth $\$ 2466 ?$
A) 2006
B) 2007
C) 2008
D) 2005

Question

Quizplus · Accepted Answer

To find when the account will be worth $2466, solve the equation $2466 = 1700 \mathrm{e}^{0.062t}$. Dividing both sides by 1700 gives $\mathrm{e}^{0.062t} = \frac{2466}{1700}$. Taking the natural logarithm of both sides, $\ln(\mathrm{e}^{0.062t}) = \ln(\frac{2466}{1700})$, simplifies to $0.062t = \ln(\frac{2466}{1700})$. Solving for $t$ gives $t \approx 6$. Therefore, the year is 2000 + 6 = 2006.

Solve -The Value of a Particular Investment Follows a Pattern A=1700e0.062t\mathrm { A } = 1700 \mathrm { e } ^ { 0.062 \mathrm { t } }A=1700e0.062t

Solve
-The Value of a Particular Investment Follows a Pattern $\mathrm { A } = 1700 \mathrm { e } ^ { 0.062 \mathrm { t } }$