castroville currently generates 44,989 tons of garbage per year, but the city is launching some recycling…

castroville currently generates 44,989 tons of garbage per year, but the city is launching some recycling initiatives to bring that number down. if, as a result, the amount of garbage decreases by 5% each year, then how much garbage will be generated annually 10 years from now? if necessary, round your answer to the nearest tenth. tons

castroville currently generates 44,989 tons of garbage per year, but the city is launching some recycling initiatives to bring that number down. if, as a result, the amount of garbage decreases by 5% each year, then how much garbage will be generated annually 10 years from now? if necessary, round your answer to the nearest tenth. tons

Answer

Explanation:

Step1: Identify the formula

The formula for exponential decay is $A = P(1 - r)^t$, where $P$ is the initial amount, $r$ is the rate of decay, and $t$ is the time. Here, $P = 44989$, $r=0.05$, and $t = 10$.

Step2: Substitute the values

$A=44989\times(1 - 0.05)^{10}=44989\times0.95^{10}$.

Step3: Calculate $0.95^{10}$

$0.95^{10}\approx0.598736939$.

Step4: Calculate $A$

$A = 44989\times0.598736939\approx26917.5$.

Answer:

$26917.5$