Question

a culture of bacteria has an initial population of 4800 bacteria and doubles every 9 hours. using the formula $p_{t}=p_{0}cdot2^{\frac{t}{d}}$, where $p_{t}$ is the population after $t$ hours, $p_{0}$ is the initial population, $t$ is the time in hours and $d$ is the doubling - time, what is the population of bacteria in the culture after 14 hours, to the nearest whole number?

Explanation:

Step1: Identify the values

$P_0 = 4800$, $t = 14$, $d=9$.

Step2: Substitute into the formula

$P_t=P_0\cdot2^{\frac{t}{d}}=4800\cdot2^{\frac{14}{9}}$.

Step3: Calculate the exponent value

First, calculate $\frac{14}{9}\approx1.5556$. Then find $2^{1.5556}$. Using a calculator, $2^{1.5556}\approx2.962$.

Step4: Calculate the final population

$P_t = 4800\times2.962 = 14217.6$.

Answer:

$14218$