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

Step-by-step explanation:

The exponential growth function is given by :-

, 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 :-

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

hence, the required inequality :

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.