Exponential and Logarithmic Functions
Finding a final amount in a word problem on exponential growth or decay
Kayleigh
A certain forest covers an area of $1800{\mathrm{km}}^2$. Suppose that each year this area decreases by $4.5\mathrm{\%}$. What will the area be after 12 years?
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Use the calculator provided and round your answer to the nearest square kilometer.
$$\prod {\mathrm{km}}^2$$
$$\times$$
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Step 1 ：A certain forest covers an area of 1800 square kilometers. Suppose that each year this area decreases by 4.5%. We are asked to find the area of the forest after 12 years.

Step 2 ：We can use the formula for exponential decay to solve this problem. The formula is $A=P(1-r{)}^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the rate of decay, and $t$ is the time.

Step 3 ：Substituting the given values into the formula, we get $A=1800(1-0.045{)}^{12}$.

Step 4 ：Calculating the above expression, we find that $A\approx 1035.888386386458$.

Step 5 ：Rounding to the nearest square kilometer, we get $A\approx 1036$.

Step 6 ：Final Answer: The area of the forest after 12 years will be approximately $\boxed{{\displaystyle 1036}}$ square kilometers.