Question

The air pressure inside Jason’s bike tires decreases by about 6% each week. The original pressure was 45 pounds per square inch (psi).

a. Write an exponential model for the air pressure in the tires.



b. What is the tire pressure after 6 weeks?

Answer 1

Compound percentage reduction can be calculated by multiplying the initial number by (1-x)^t where x is the percentage reduction (/100, i.e. 1% reduction is 0.01), and t is the number of times it has reduced.

So:
a) $p=45(1-0.06)^t=45*0.94^t$
Where t is the number of weeks.

We can then just substitute in to work out the final pressure:
b) p = 45*0.94^6 = 31psi