CL. 7-120. Below are several situations that can be described using exponential

Question

CL. 7-120. Below are several situations that can be described using exponential functions. They represent a smail sampling of the situations where quantities grow or decay by a constant percentage over equal periods of time. For each situation (a) through (d): Find an appropriate unit of time (such as days, weeks, years) . Find the multiplier that should be used. . Identify the initial value. Write an exponential equation in the form f(x)- ab that represents the growth or decay. A house purchased for $120,000 has an annual appreciation of 6%. increases at a rate of 22% per hour. The value of a car with an initial purchase price of $12.250 depreciates a. b. The number of bacteria present in a colony is 180 at noon, and it c. by i 1 % per year. d. An investment of $1000 earns 6% annual interest, compounded monthly

Explanation / Answer

a) intial price = $ 120,000 , annual deprcication = 6%

-years (x)

intial value a= $ 120,000

b = 1- 0.06 = 0.94

So, f(x) = 120,000(0.94)^x

b) hrs (x)

intial value , a = 180

b = (1+ 0.22) = 1.22

So, f(x) = 180(1.22)^x

c) years (x)

intial value , a =$ 12,250

b = 1- 0.11

So, f(x) = 12250(0.89)^x

d) no. of months , x

intial value , a = $ 1000

b = 1 + 0.06/12 = 1.005

So, f(x) = ab^x = 1000(1.005)^12x

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