Question

this year, seaside recycled 21,600 tons of material. if this amount increases by 9% each year, how much material will be recycled 7 years in the future? if necessary, round your answer to the nearest tenth. tons submit

Explanation:

Step1: Identify the formula for exponential growth

The formula for exponential growth is $A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the initial principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the time in years.
Here, $P = 21600$, $r = 0.09$ (since 9% = 0.09), and $t = 7$.

Step2: Substitute the values into the formula

Substitute $P = 21600$, $r = 0.09$, and $t = 7$ into the formula:
$A = 21600(1 + 0.09)^7$

Step3: Calculate $(1 + 0.09)^7$

First, calculate $1 + 0.09 = 1.09$. Then, calculate $1.09^7$. Using a calculator, $1.09^7 \approx 1.828039$.

Step4: Calculate the final amount $A$

Multiply $21600$ by $1.828039$:
$A = 21600 \times 1.828039 \approx 39485.6424$

Step5: Round to the nearest tenth

Rounding $39485.6424$ to the nearest tenth gives $39485.6$.

Answer:

39485.6