A school laboratory keeps two sealed gas canisters

MATHEMATICS · Subjective · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

A school laboratory keeps two sealed gas canisters. The manufacturer prints the following statements on the labels: (i) “The initial pressure

P_{0}

(in pascals) and the current pressure

P

(in pascals) satisfy

P=1.2^{t}P_{0}

, where

t

is the time in hours after sealing.” (ii) “After

t

hours the pressure doubles, i.e.

\dfrac{P}{P_{0}}=2

.” Answer the following with explicit mathematical steps: (a) Rewrite the statement in part (i) in logarithmic form making

t

the subject. (b) Using the result from part (a), find the exact value of

t

(correct to two decimal places) mentioned in part (ii).