The Boeing 747-8 Intercontinental Jet can carry approximately 422,000 gallons of gasoline, making it possible for the jet to travel 14,430 kilometers before needing to refuel. Create a linear model that represents the amount of gasoline on the plane, in gallons, as a function of the flight time, in hours.

Step-by-step explanation:

The travel time is found dividing the flight traveled distance by cruise speed:

A Boeing 747-8 has a cruise speed of 914 kilometers per hour. Then:

The maximum distance as function of the quantity of gallons of gasoline is estimated by the following linear model:

Finally, the required expression is:

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