Question

You invest $2,500 in an account that grows 5% each year. what will be your investment amount after 6 years?

Answer 1

Answer:  b. $3,374.65

Step-by-step explanation:

The exponential equation of growth (continuously) is given by :-

$y=Ae^{rx}$, where A is the initial amount, r is the rate of growth ( in decimal) and x is the time period.

Given : You invest $2,500 in an account that grows 5% each year.

i.e.  A= $2,500  and r= 5%=0.05

Then, the equation model this situation will be :-

$y=2500e^{0.05x}=2500(1.05)^x$

Now, At x= 6

$y=2500e^{0.05\times6}\\\\\Rightarrow\ y=2500e^{0.3}=3374.64701894\approx3374.65$

Hence, the investment amount after 6 years will be $3,374.65.