Question

A quantity with an initial value of 920 decays continuously at a rate of 4% per second.

What is the value of the quantity after 0.8 minutes, to the nearest hundredth?

Answer 1

134.88

Explanation:

Write function:

f(t)=920e r/t(exponent)

R: decays 4% > -0.04

substitute r in the function for -0.04

0.8 minutes = 48 seconds

plug In t=48

F(48)= 920e -0.04(48) <(exponents)

=134.878405159922

round to 134.88 and that’s the answer.

Answer 2

first off, the "elapsed time" unit and the "rate" unit must correspond, in this case the decay rate is 4% per second, whilst the elapsed time is in minutes, so let's change that to seconds, hmmmm there are 60 seconds in 1 minute so in 0.8 minute there are 0.8*60 = 48 seconds.

`\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &920\\ r=rate\to 4\%\to (4)/(100)\dotfill &0.04\\ t=\textit{elapsed time}\dotfill &48\\ \end{cases} \\\\\\ A=920(1-0.04)^(48)\implies A=920(0.96)^(48)\implies A\approx 129.66`