Question

a bike tire just ran over a nail, and it is losing pressure at a rate of 10% every minute. the tire pressure is currently 1,060 kilopascals. what will it be in 4 minutes? if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Define decay formula

This is exponential decay. The formula is $P(t) = P_0(1-r)^t$, where $P_0=1060$, $r=0.10$, $t=4$.

Step2: Calculate remaining factor

$(1-0.10)^4 = 0.9^4 = 0.6561$

Step3: Compute final pressure

$P(4) = 1060 \times 0.6561$
$P(4) = 695.466$

Step4: Round to nearest tenth

Round $695.466$ to 1 decimal place: $695.5$

Answer:

695.5 kilopascals