1. Solve and show all your work. a. e -3t = 150 b. 3 x+2 = 30 3. In 2010, the po
ID: 3029907 • Letter: 1
Question
1. Solve and show all your work.
a. e-3t = 150
b. 3x+2 = 30
3. In 2010, the population in the United States was approximately 308,747,716. Its exponential growth rate is approximately 2.4%.
a. Find the exponential growth function, P(t), for this situation, where t is number of years since 2010. Answer should be in correct function notation.
b. Estimate the population of the United States for the year 2014.
c. In what year will the population of the United States be 400,000,000? Solve using algebraically.
d. Find the doubling time.
Explanation / Answer
a) e^-3t = 150
taking natural log on both sides
-3t = ln 150
-3t = 5.010
t = 5.010 / -3 = -1.670
t = -1.670
b) 3x + 2 = 30
subtracting 2 from both sides
3x = 28
dividing both sides by 3
x = 28/3
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