During the past 10 years, the amount of money, m (in billions of dollars), spent in north america by car dealerships advertising their product can be modeled by the equation m = 1.2e0.25t  + 0.13. in what year was about $19 billion (m = 19) spent by car dealerships in advertising?

From the given Equation :
M = 1.2e^0.25t + 0.13

Substitute M = 19 into the above equations,
We get,
19 = 1.2e^0.25t + 0.13
Rearrange it for t.
19 - 0.13 = 1.2e^0.25t
Subtracting 0.13 on both sides
18.87 = 1.2e^0.25t
Dividing by 1.2 into both sides
18.87/1.2 = e^0.5t
15.725= e^0.5t
Taking natural log on both sides:
we get;
ln 15.725 = lne^0.5t
Applying logarithmic identities:
ln 15.725 = 0.5t
t = ln 15.725/0.5
t = 5.51 years
As t is a decimal number, so the year where the amount of money would be $19 billion is between the 5th and the 6th year.

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