Homework SourseSuppose that Montes Tatoo parlor had profits of 23000 in 198
Suppose that Monte\'s Tatoo parlor had profits of $23,000 in 1988 and $7,000 in 1994.
a)Monte\'s financial advisor decides to model the company\'s profits with a linear model, assuming the rate of change remains constant. Write a linear equation to model profits using above data
b)Suppose now that new info. indicates that Monte\'s profits reached an all-time low point in 1994, and are about to recover. His advisor decides to model profits with a quadratic equation. Write a quadratic equation to model profits
c)Suppose now that new info. indicates profits will continue to decline exponetially at the same annual rate from 1988 to 1994. Advisor decides to model profits with an equation of exponential decay compounded annually. Write a function of exponential decay to model profits.
a)Monte\'s financial advisor decides to model the company\'s profits with a linear model, assuming the rate of change remains constant. Write a linear equation to model profits using above data
b)Suppose now that new info. indicates that Monte\'s profits reached an all-time low point in 1994, and are about to recover. His advisor decides to model profits with a quadratic equation. Write a quadratic equation to model profits
c)Suppose now that new info. indicates profits will continue to decline exponetially at the same annual rate from 1988 to 1994. Advisor decides to model profits with an equation of exponential decay compounded annually. Write a function of exponential decay to model profits.
Solution
a) slope is 7,000-23,000/6= -8,000/3 So y= 23,000- (8,000/3) x where x is number of years since 1988 b) We have y= A(x-k)^2 +h where (k,h) is vertex. (6, 7,000) is vertex since it is low point. 23,000= a (-6)^2 + 7,000 a= 16,000/36= 4,000/9 So we have Y= 4000/9 (x- 6)^2 +7,000 c) We have declined 7,000/23,000 to .3043 of the original amount in 6 years. So we have (.3043)^(1/6) .82105 per year We have Y= 23,000*(.82015)^x where x is the number of years since 1988.
