investments increase exponentially by about 27% every 3 years. if you start with a $1000 investment, how…

Explanation:

Step1: Determine the initial amount

The initial investment is $1000$, so the first - blank value is $1000$.

Step2: Determine the growth rate

The investment increases by $27%=0.27$ every 3 years, so the value in the second - blank is $0.27$.

Step3: Determine the number of 3 - year periods

The time period is 12 years. Since the growth occurs every 3 years, the number of 3 - year periods $n=\frac{12}{3}=4$. So the value in the third - blank is $4$.

Step4: Calculate the future amount

The formula for exponential growth is $A = P(1 + r)^n$, where $P$ is the principal amount, $r$ is the growth rate per period, and $n$ is the number of periods. Substituting $P = 1000$, $r=0.27$, and $n = 4$ into the formula: $A=1000\times(1 + 0.27)^4=1000\times1.27^4=1000\times2.60140561\approx2601.41$

Answer:

The future amount is $1000(1 + 0.27)^4$ and the value after 12 years is approximately $$2601.41$