Rita will rent a car for the weekend. she can choose one of two plans. the first plan has no initial fee but costs $0.90 per mile driven. the second plan has an initial fee of $60 and costs an additional $0.40 per mile driven. how many miles would rita need to drive for the two plans to cost the same?

Let M = #miles driven

Plan 1:   .50M + 70  = total cost

Plan 2    .70M = total cost

To know how far she would drive to have an equal cost for either plan just set the equations equal to each other

.70M = .50M + 70

subtract .50M from both sides

.20M = 70

M = 70/.20 = 350 miles

Check the answser:

Plan 1:  .50(350) + 70 = 175 + 70 = $245

Plan 2:  .7(350) = $245

they are equal so our answer checks as correct

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