Maria studied the traffic trends in India. She found that the number of cars on the road increases by 10% each year. If there were 80 million cars in year 1 of her study, how many more cars were on the road in year 3 compared to year 2?

Step-by-step explanation:

Let's first find the exponential function that models the situation in year one. The exponential standard form is

where a is the initial value and b is the growth/decay rate in decimal form. If it is growth it is added to 100% of the initial value; if it is decay it is taken away from 100% of the initial value. We are told that the number of cars in year one was 80 million, so

a = 80 (in millions)

If b is increasing by 10%, then we are adding that amount to the initial 100% we started with to give us 100% + 10% = 110% or, in decimal form, 1.1

The model for our situation is

where y is the number of cars after x years goes by. We want to find the difference between years 3 and 2, so we will use our model twice, replacing x with both a 2 and then a 3 and subtracting.

When x = 2:

and

y = 80(1.21) so

y = 96.8 million cars

When x = 3:

and

y = 80(1.331) so

y = 106.48 million cars

The difference between years 3 and 2 is

106.48 - 96.8 = 9.68 million cars

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^

x=half

step-by-step explanation: