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

Answer:

420.11 kilo-pascals.

Step-by-step 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.

$5\%=\frac{5}{100}=0.05$

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.