Question

A bike tire just ran over a nail, and it is losing pressure at a rate of 5% every minute. The tire pressure is currently 490 kilopascals. What will it be in 3 minutes

Answer 1

420.11 kilo-pascals.

Explanation:

We have been given that a bike tire just ran over a nail, and it is losing pressure at a rate of 5% every minute. The tire pressure is currently 490 kilo-pascals. We are asked to find the tire pressure in 3 minutes.

We will use exponential decay formula to solve our given problem.

`y=a(1-r)^x`, where,

y = Final value,

a = Initial value,

r = Decay rate in decimal form,

x = Time.

Let us convert 5% into decimal.

`5\%=(5)/(100)=0.05`

Initial value is 490. Upon substituting our given values in above formula, we will get:

`y=490(1-0.05)^x`

To find tire pressure in 3 minutes, we will substitute
`x=3` and solve for y as:

`y=490(0.95)^3`

`y=490(0.857375)`

`y=420.11375\approx 420.11`

Therefore, the tire pressure will be approximately 420.11 kilo-pascals in 3 minutes.