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 $10,000$?

Determine if the function is an exponential function.  

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

$f\(\left\)(x\(\right\))=\(\left\)(\(\frac\)12\(\right\))^{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 triple in size?

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.

${\log }_{6}60$

Changing bases Convert the following expressions to the indicated base.

$\ln \mid x\mid$ using base 5