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Problem #1
Identify the initial amount, a, and growth factor, b, in each exponential function. Break b into (1 - r) where r is the rate of growth. Give r as a percentage.
Formula, y = a(b)x
y = 1.25(0.98)x
Answer:
a = 1.25
b = (1 - .02)
r = 1 - 0.98 = .02 = 2%
Problem #2
Identify the initial amount, a, and growth factor, b, in each exponential function. Break b into (1 - r) where r is the rate of growth. Give r as a percentage.
Formula, y = a(b)x
y = 3.25(0.95)x
Answer:
a = 3.25
b = (1 - .05)
r = 1 - 0.95 = .05 = 5%
Problem #3
Identify the initial amount, a, and growth factor, b, in each exponential function. Break b into (1 - r) where r is the rate of growth. Give r as a percentage.
Formula, y = a(b)x
y = 2.05(0.975)x
Answer:
a = 2.05
b = (1 - .025)
r = 1 - 0.975 = .025 = 2.5%
Problem #4
A farmer is able to depreciate the value of machinery as part of his income tax return. If the farmer has a tractor valued at $35,000.00 that depreciates at a rate of 10% per year, what will be the tax value of his tractor in 5 years?
y = C(1 - r)x
y = 35000(1 - .10)5
y = 35000(.90)5
Answer:
y = 20667.15
The tax value of the tractor in 5 years will be $20, 667.15.
Problem #5
The population of Cleveland, ohio was 478,403 in 2000. Claveland has been experiencing a population decline of 0.6% per year since 1990. What will be the projected population of Cleveland in 2010?
y = C(1 - r)x
y = 478,403(1 - .006)10
y = 478,403(.994)10
Answer:
y = 450462
The projected population of Cleveland in 2010 will be 450,462.