1 Solve and show all your work a e3t 150 b 3x2 30 3 In 201

1. Solve and show all your work.

a. e^-3t = 150

b. 3^x+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.

Solution

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