The sales for exercise equipment in a country were $1826 million in 1990 and $51
ID: 2883808 • Letter: T
Question
The sales for exercise equipment in a country were $1826 million in 1990 and $5120 million in 2005.
(a) Use the regression feature of a graphing utility to find an exponential growth model and a linear model for the data. (Use y to represent sales in millions of dollars and t to represent years after 1990. Round your values to four decimal places.)
(b) Use the exponential growth model to estimate the sales in 2018. (Round your answer to one decimal place.)
$ million
(c) Use the linear model to estimate the sales in 2018. (Round your answer to one decimal place.)
$ million
(d) Use a graphing utility to graph the models from part (a). Which model is more accurate?
A)The exponential model is more accurate.
B)The linear model is more accurate.
C)More information is needed.
exponential model y = linear model y =Explanation / Answer
a) For linear data
y = ax + b
1826 = a(1990) + b ----- (i)
5120 = a(2005) + b ------ (ii)
subtracting 1 from 2 we get
15a = 3294
a = 219.6
b = 1826 - (219.6)(1900) = -415414
Hence y = 219.6x - 415414
For exponential model
y = Ae^(ax)
1826 = Ae^(1990a)
5120 = Ae^(2005a)
e^(15a) = 2.8039
15a = ln(2.8039)
a = 1/15 * ln(2.8039) = 0.06873
1826 = Ae^(0.06873*1990)
A = 4.007 * 10^(-57)
b)
y = 4.007 * 10^(-57) * e^(0.06873*2018)
=> 12615.1 million
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