In a certain state, there are currently 5,902,060 acres of farmland. This area is decreasing at a rate of 4.3% every year. Select the correct equation that models the situation after t years.

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Mathematics

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1 February, 15:34

In a certain state, there are currently 5,902,060 acres of farmland. This area is decreasing at a rate of 4.3% every year. Select the correct equation that models the situation after t years.

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Matias Robertson · Answer 1

y=5,902,060 * (.957) ^t

Step-by-step explanation:

Since the original amount would be decreasing and it's an exponential one, hence the "every year", we can determine that it's an exponential decay equation.

The exponential delay equation is y=A * (1-r) ^t. The y is the remaining amount, A is the original amount, r is the rate in decimal form, and t is for years. "1-r" is for decreasing rates and "1+r" is for increasing rates.

First thing we need to do is turn the rate, 4.3%, from a percentage to a decimal. You can do this by moving the decimal two places to the right, which gives you 0.043.

Now plug the numbers into the equation.

y=5,902,060 * (1-0.043) ^t

Simplify what's inside the parenthesis and get your final equation.

y=5,902,060 * (.957) ^t