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lynne walks dogs everyday to earn money. the fees she charges per month are 1 dog $40, 2 dogs $37.25, 3 dogs $34.50 each, 4 dogs $31.75 each. a pet store wants her to walk 8 dogs. if the pattern continues, how much will lynne charge to walk each of the 8 dogs?

Respuesta :

Gladys0923
1 dog = $40 2 dogs = $37.25 3 dogs = $34.50 4 dogs = $31.75 5 dogs = $29 6 dogs = $26.25 7 dogs = $23.50 8 dogs = $20.75 Pattern is minus $2.75
JeanaShupp

Answer: $20.75


Step-by-step explanation:

Given : Lynne walks dogs everyday to earn money.

The fees she charges per month are 1 dog $40 each , 2 dogs $37.25 each, 3 dogs, $34.50 each and 4 dogs $31.75 each.

let x be the number of dogs and f(x) be fee she charged per month.

We know that, the rate of change of f(x), if pattern continues

[tex]=\frac{f(4)-f(1)}{4-1}=\frac{\$31.75-\$40}{4-1}=\frac{-\$8.25}{3}=-\$2.75[/tex]

Thus she decreases her fee $2.75 per on  increment of number of dogs

For x=8 , to find f(8), we consider same pattern to 8 dogs.

Thus,

[tex]\frac{f(8)-f(1)}{8-1}=-\$2.75\\\Rightarrow\frac{f(8)-40}{7}=-2.75\\\Rightarrow\ f(8)-40=7\times-2.75\\\Rightarrow\ f(8)-40=-19.25\\\Rightarrow\ f(8)=40-1925=\$20.75[/tex]

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