1. A savings account with a current balance of $5,000 earns 2.75% annual interest, compounded continuously. To the nearest dollar, what will be the account balance in 10 years?
GROWTH.
a=?,P=5,00,r=2.75,t=10
A=P(1+rt)
A=5,000(1+2.75*10)
A=5,000(1+27.5)
A=5,000(28.5)
A=142,500
Since the balance is $5000 and earns 2.75% annual interest, the money will increase.
2.According to the U.S. Census Bureau (http://www.census.gov/), the population of Texas is growing at a faster rate than any other state in the United States. In 2012 the population of Texas was approximately 26,000,000 people and was growing at a rate of 2.10% per year. At the current growth rate, what will the population of Texas be in the year 2030? Round the answer to the nearest million people. (Note: Use continuous compounding.)
3.The value of a new car decreases exponentially. Suppose you buy a new car for $32,000, and the value of the car decreases at a rate of 20% per year. Find the value of the car after 5 years. Round the answer to the nearest thousand dollars.
DECAY
v = future value
c = current value
r = depreciation rate per period
t = number of periods
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v = 32000*(1-0.20)^5
v = 10485.76
4.Suppose you deposit $10,000 into a savings account with 3.5% compound interest compounded each month. Find the account balance in 50 years. Round the answer to the nearest thousand dollars.
GROWTH
v = final value
p = initial (principal) value
r = interest rate (as a decimal)
n = number of compounding periods per year
t = number of years
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v = 10000( 1 + (0.035/12) )^(12*50)
v = 57399.66
5.On January 1, 2010, the population of a small town called Riley was 1,250. Its population has been decreasing at a steady rate of 8% per year. According to this model, what was Riley’s population on January 1, 2000? Round the answer to the nearest person. (Hint: Use the continuously compounding formula.)
DECAY
A = Pe^rt
A = 1250
r = -0.08
t = 10
1250 =...