Question

A huge ice glacier in the Himalayas initially covered an area of 454545 square kilometers. Because of changing weather patterns, this glacier begins to melt, and the area it covers begins to decrease exponentially.
The relationship between AAA, the area of the glacier in square kilometers, and ttt, the number of years the glacier has been melting, is modeled by the following equation.
A=45e^{-0.05t}A=45e
−0.05t
A, equals, 45, e, start superscript, minus, 0, point, 05, t, end superscript
How many years will it take for the area of the glacier to decrease to 151515 square kilometers?
Give an exact answer expressed as a natural logarithm.

Answer 1

Answer: t=-20ln(1/3)

Step-by-step explanation:

Answer 2

So, the time taken is  22 years.

Given that,

A huge ice glacier in the Himalayas has initially covered an area $A_0=45 km^2$

Given relationship is,

$A=45e^{-0.05t}$

Also, the area of the glacier decreases to 15 km per square then,

$15=45e^{-0.05t}\\e^{-0.05t}=\frac{1}{3} \\t=\frac{ln\frac{1}{3} }{-0.05} \\t=21.97\\t\approx 22 y$

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