The area of a lake is decreasing by 2% each YEAR and can be modeled by A(t) =&nbsp;11⋅(.98)t11⋅(.98)t.&nbsp;&nbsp;&nbsp;&nbsp;By what factor does the area decrease each MONTH?&nbsp;&nbsp;&nbsp;

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The area of a lake is decreasing by 2% each YEAR and can be modeled by A(t) =&amp;nbsp;11⋅(.98)t11⋅(.98)t.&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;By what factor does the area decrease each MONTH?&amp;nbsp;&amp;nbsp;&amp;nbsp;

RizerMix · Accepted Answer

The given model for the area of the lake is: A(t)=11·(0.98)t, where A(t) represents the area at time t in years.To find the factor by which the area decreases each month, we need to determine the relationship between months and years. There are 12 months in a year, so we can divide the annual decrease by 12 to find the monthly decrease.Let&#039;s calculate the factor by which the area decreases each month:A(t)=11·(0.98)tTo express the time in months, we divide t by 12:A(t12)=11·(0.98)t12Now, we can rewrite the equation in terms of months:A(tmonths)=11·(0.98)tmonths12Comparing this equation to the original equation, we can see that the factor by which the area decreases each month is (0.98)112.Therefore, the area of the lake decreases each month by a factor of (0.98)112.

The area of a lake is decreasing by

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