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Exponential Functions

Identify the variables, identify the constants, write the function, solve the equation and write a complete answer.
 
Suppose the acreage of forest is decreasing by 6.5% per year because of development. If there are currently 10,500,000 acres of forest, determine the amount of forest land after 15 years.

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Andre W. | Friendly tutor for ALL math and physics coursesFriendly tutor for ALL math and physics ...
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"Decreasing by 6.5% per year" means decreasing to (100-6.5)%=93.5%, or .935, of the previous year's value.
After two years, the acreage will have decreased to .9352 of the original value (10,500,000 acres), and after 15 years it will have decreased to .93515 of its original value, namely
.93515*10,500,000 ≈ 3,830,000 acres.
William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...
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Dear Jenna,
 
In general, for any situation where there is exponential decay, the equation would be
 
At = A0e-kΔt
 
where At is the amount remaining after time Δt has passed, A0 is the initial amount, and k is a constant, in this case 6.5% of 0.065.
 
At = (10,500,000 acres)*e(-0.065)*(15 years) = (10,500,000 acres)*(0.377192) = 3,960,519 acres