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?
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.
