Question

1. for a period of time, e. coli bacteria in a culture grows exponentially. if the continuous growth rate is 1% per minute and the current population is 165.0 million, what will the population be 6 minutes from now?

f(x)=ae^{rx}

Explanation:

Step1: Identify the formula variables

The formula for continuous - growth is $f(t)=ae^{rt}$, where $a$ is the initial amount, $r$ is the growth rate, and $t$ is the time. Here, $a = 165$ (in millions), $r=0.01$ (since 1% = 0.01), and $t = 6$.

Step2: Substitute the values into the formula

Substitute $a = 165$, $r = 0.01$, and $t = 6$ into $f(t)=ae^{rt}$, we get $f(6)=165\times e^{0.01\times6}$.

Step3: Calculate the exponent part

First, calculate $0.01\times6 = 0.06$. Then, find the value of $e^{0.06}$. Using a calculator, $e^{0.06}\approx1.061836547$.

Step4: Calculate the final population

Multiply 165 by $e^{0.06}$: $f(6)=165\times1.061836547\approx175.203030255\approx175.2$ (in millions).

Answer:

175.2 million