The graph shows your distance from home on a day trip to a lake which is 80 miles away. which statement is true about your trip?

a. you spent 6 hours at the lake.

b. you were traveling uphill for the first 2 hours of the trip.

c. it took you 2 hours to reach the lake.

d. you returned home at 8pm

c. it took you 2 hours to reach the lake

b is the answer that makes most sense

step-by-step explanation:

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