Grayson's Garage charges $40 per hour to do car repairs plus the cost of the parts.

a. Write an equation to model this situation using h to represent the number of hours the repairs take, p to represent the costs of the parts and, c to represent the total cost of the repairs.

b. What will the cost of the repairs be if the parts cost $165 and it takes 3 hours to do the repairs? Show your work and label.

(a) c = 40h + p

(b) $285

Step-by-step explanation:

(a)

Total Cost = (Cost per hour x Number of Hours) + Total Cost of Parts

c = 40h + p

(b)

For this case, p = $165 and h = 3:

c = 40*3 + 165 = $285

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places