Question 769221
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The weight in kilograms,W, of a female African elephant at age t years is given by W(t)=2600(1-0.51e^-0.075t). Estimate the age, to the nearest year, of an adult female African elephant weighing 1800 kilograms.
Ans:
Substituting for Weight as 1800 in the equation, we get
{{{1800 = 2600*(1 - 0.51*e^(-0.075t))}}}
Simplifying
{{{(1 - 0.51*e^(-0.075t)) = 1800/2600 = 9/13}}}
{{{0.51*e^(-0.075t) = 0.51/(e^(0.075t)) = 1 - (9/13) = 0.3077}}}
{{{e^(0.075t) = 0.51/0.3077 = 1.6575}}}
Taking natural logarithms of both sides
{{{0.075*t = ln(1.6575) = 0.5053}}}
{{{t = 0.5053/0.075 = 6.737}}}
So age of the elephant rounded off to nearest year is 7 years.

Hope you got it :)
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