Question

The number of cars that passed through a tollbooth prior to 6 a.m. is 1,380. The number of cars that pass through the tollbooth from 6 a.m. through the morning rush hour increases by 46% every hour. Which of the following inequalities can be used to determine the number of hours, t, after 6 a.m. when the number of cars that have passed through the tollbooth is over 4,300?

1,380(1.46)t > 4,300

1,380(1.46)t < 4,300

1,380(0.54)t < 4,300

1,380(0.54)t > 4,300

Answer 1

Answer:
`1,380(1+0.46)^t>4,300`

Explanation:

The exponential growth function is given by :-

`y=A(1+r)^t`, where A is the initial value , r is the rate of growth and t is time.

Given : The number of cars that passed through a tollbooth prior to 6 a.m. is 1,380.

i.e. A = 1,380

The number of cars that pass through the tollbooth from 6 a.m. through the morning rush hour increases by 46% every hour.

i.e. r=46%=0.46

Now, the function to determine the number of hours, t, after 6 a.m. when the number of cars that have passed through the tollbooth :-

`1,380(1+0.46)^t`

For number of cars that have passed through the tollbooth is over 4,300, we have

`1,380(1+0.46)^t>4,300`

hence, the required inequality :
`1,380(1+0.46)^t>4,300`

Answer 2

the answer is A since you are trying to solve for t, you want the greater than sign to be facing towards the variable.