Problem

Data points $(x, y)$ are given. (a) Draw a scatt…

Problem 58 Hard Difficulty

When a camera flash goes off, the batteries immediately begin to recharge the flash's capacitor, which stores electric charge given by
$$Q(t)=Q_{0}\left(1-e^{-t / a}\right)$$
(The maximum charge capacity is $Q_{0}$ and $t$ is measured inseconds.)
(a) Find the inverse of this function and explain its meaning.
(b) How long does it take to recharge the capacitor to 90$\%$ of capacity if $a=2 ?$

Answer

(a) $t=-a \ln \left[1-\frac{Q}{Q_{o}}\right]$
(b) $\approx 4.605$ seconds

Related Courses

Calculus 1 / AB

Biocalculus Calculus for the Life Sciences

Chapter 1

Functions and Sequences

Section 5

Logarithms; Semilog and Log-Log Plots

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Video Transcript

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