6.4 q4.) how much weekly profit (to the nearest dollar) will the agency have if 75 cars are sold per week?

The first integral in the table matches the form in the problem, with

... u = x, a = 2, b = 5.

Then the profit function is

... p(x) = 2(15x-4)/(375)√((2+5x)³) - 1501.09

(Without the added constant, the function p(1) evaluates to about 1.09.)

A graph shows the number of sales required for a $12000 profit is about 47 cars.

Sale of 75 cars per week will result in a profit of about p(75) ≈ $42,263.

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