Question Type 11: Performing simple calculations with an exponential model Exercises

For the model $P(t)=100e^{-t}+20$, determine $\lim_{t\to\infty}P(t)$.

Find the initial amount of bacteria in the model $A(t) = 5e^{-3t} + 9$.

Calculate the amount at $t=2$ for the model $A(t) = 12e^{0.8t} + 3$.

A drug concentration decays as $C(t)=5e^{-0.1t}$ mg/L. Find its half-life.

Given $A(t)=50e^{-0.2t}+10$, find the time $t$ when $A(t)=30$.

A hot object cools as $T(t)=20+80e^{-0.3t}$. Find the time when $T(t)=50\,^{\circ}\mathrm{C}$.

In the model $A(t)=500e^{-0.2t}+50$, find the time $t$ when $A(t)=100$.

In the model $P(t)=200e^{0.1t}+50$, find the time $t$ when $P(t)=350$.

Radioactive decay is modeled by $N(t)=100e^{-0.693t/5}$. Find the time when $N(t)=25$.

For $C(t)=10e^{-0.5t}+2$, how long until $C(t)$ is within $0.5$ of its long-term value?

The population grows according to $P(t)=1000e^{0.05t}$. Determine the doubling time.