A culture of bacteria has a population of $150$ cells when it is first observed. The population doubles every $12~\text{hr}$, which means its population is governed by the function $p\left(t\right)=150\cdot{2^{\frac{t}{12}}}$, where $t$ is the number of hours after the first observation.
How long does it take the population to triple in size?

Determine if the function is an exponential function.  

If so, identify the power & base, then evaluate for $x=4$ .

$f\left(x\right)=3\left(1.5\right)^{x}$

Determine if the function is an exponential function.  

If so, identify the power & base, then evaluate for $x=4$ .

$f\left(x\right)=\left(\frac12\right)^{x}$

Graph the given function.

$g\left(x\right)=e^{x+3}-1$

A culture of bacteria has a population of $150$ cells when it is first observed. The population doubles every $12~\text{hr}$, which means its population is governed by the function $p\left(t\right)=150\cdot{2^{\frac{t}{12}}}$, where $t$ is the number of hours after the first observation.

What is the population $4~\text{days}$ after the first observation?

A culture of bacteria has a population of $150$ cells when it is first observed. The population doubles every $12~\text{hr}$, which means its population is governed by the function $p\left(t\right)=150\cdot{2^{\frac{t}{12}}}$, where $t$ is the number of hours after the first observation.

How long does it take the population to reach $10,000$?

Solve each equation.

$48=6e^{4k}$

Solve each equation.

$7^{y-3}=50$

Write the following logarithms in terms of the natural logarithm. Then use a calculator to find the value of the logarithm, rounding your result to four decimal places.

${\log }_{6}60$