Question

this year, newton recycled 79,270 tons of material. if this amount increases by 8% each year, how much material will be recycled 10 years in the future? if necessary, round your answer to the nearest tenth. tons submit

Explanation:

Step1: Identify the formula for compound growth

The formula for compound growth is $A = P(1 + r)^t$, where $P$ is the principal (initial amount), $r$ is the annual growth rate (as a decimal), and $t$ is the number of years.
Here, $P = 79270$, $r = 0.08$ (since 8% = 0.08), and $t = 10$.

Step2: Substitute the values into the formula

Substitute $P = 79270$, $r = 0.08$, and $t = 10$ into the formula $A = P(1 + r)^t$.
So, $A = 79270(1 + 0.08)^{10}$.

Step3: Calculate $(1 + 0.08)^{10}$

First, calculate $(1.08)^{10}$. Using a calculator, $(1.08)^{10}\approx2.158925$.

Step4: Multiply by the initial amount

Multiply 79270 by 2.158925: $79270\times2.158925 \approx 79270\times2.158925$.
Calculating this, $79270\times2.158925 \approx 171136.0$ (rounded to the nearest tenth).

Answer:

171136.0