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?

First, you have to formulate an equation from the problem statement. Since, the equation is already given for you, you could skip this step. Then, substitute M=19 in the equation to determine t in years:

19 = 1.2e^0.25t + 0.13

19 - 0.13 = 1.2e^0.25t

18.87 = 1.2e^0.25t

18.87/1.2 = e^0.5t

15.725 = e^0.5t

Take ln on both sides:

ln 15.725 = lne^0.5t

Applying logarithmic identities:

ln 15.725 = 0.5t

t = ln 15.725/0.5

t = 5.51 years

Therefore, the year where the amount of money in $19 billion is in between the 5th and 6th year.