Scenario: A farm in Plainville, TX will ship fruit to the distribution plant in Dallas. The farm is 350 miles from the plant 1. The table below shows part of a trip that Travis and Roy made from the farm to the distribution plant Time h (hours) Distance d (miles) 2 230 2.5 200 3 170 140 a. Determine the rate of change of the data in the table.

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

part a: 1.08

part b: 27.59