A. As you walk to your car, you notice that your tire is nearly flat! The initial psi level yesterday was 40 but it is now only 38 today. If this trend continues and the tire keeps losing the same percentage of air, how much should be left at the end of the week rounded to 1 decimal? (7 days later)

B. In fashion, clothing can quickly go out of style once it has left the runway. If an outfit (a pair of sweatpants) that costs $1250 loses its value by nearly 21% each month, solve for the number of months that it takes for the sweatpants to only cost $25. Round to the nearest month.

C. You can model that you expect a 1.25% raise each year that you work for a certain company. If you currently make $40,000, how many years should go by until you are making $120,000? (Round to the closest year.)

Step-by-step explanation:

A) initial psi level = 40

Today, psi level = 38

Amount by which it decreased is 40 - 38 = 2 psi

Percentage by which it reduced is

2/40 × 100 = 5% or 0.05

The exponential model expression is

A = (1 - r)^t

where

A represents the final value after t days

P represents the initial value

r represents the rate of decrease

Therefore, when t = 7, then

A = 40(1 - 0.05)^7

A = 40(0.95)^7

A = 27.9 psi

B) initial cost = 1250

r = 21% = 21/100 = 0.21

The exponential model expression is

A = 1250(1 - 0.21)^t

Where

t represents the number of months

A represents final cost after t months

P represents initial cost

r represents rate

If A = $25, then

25 = 1250(0.79)^t

25/1250 = 0.79^t

0.02 = 0.79^t

Taking log of both sides, it becomes

Log 0.02 = tlog0.79

- 1.699 = - 0.102t

t = - 1.699/-0.102

t = 17 months

C) initial amount = $40000

r = 1.25% = 1.25/100 = 0.0125

The exponential model expression is

A = 40000(1 + 0.0125)^t

When A = $120000, then

120000 = 40000(1.0125)^t

120000/40000 = (1.0125)^t

3 = (1.0125)^t

Taking log of both sides, it becomes

Log 3 = t log 1.0125

0.477 = 0.0054t

t = 0.477/0.0054t

t = 88 years