A culture of bacteria has an initial population of 4800 bacteria and
doubles every 9 hours. Using the formula , where is the
population after hours, is the initial population, is the time in
hours and is the doubling time, what is the population of bacteria in the
culture after 14 hours, to the nearest whole number?

Ask by Blake Luna. in the United States

Mar 21,2025

Question

A culture of bacteria has an initial population of 4800 bacteria and
doubles every 9 hours. Using the formula , where is the
population after hours, is the initial population, is the time in
hours and is the doubling time, what is the population of bacteria in the
culture after 14 hours, to the nearest whole number?

Ask by Blake Luna. in the United States

Mar 21,2025

UpStudy AI · Accepted Answer

We start with the formula  
$$
P_t = P_0 \cdot 2^{\frac{t}{d}},
$$  
where  
$$
P_0 = 4800, \quad t = 14 \text{ hours}, \quad d = 9 \text{ hours}.
$$

Substitute the values into the formula:  
$$
P(14) = 4800 \cdot 2^{\frac{14}{9}}.
$$

Calculate the exponent:  
$$
\frac{14}{9} \approx 1.5556.
$$

Now, evaluate the power of 2:  
$$
2^{1.5556} = e^{1.5556 \ln 2}.
$$  
Since $$\ln 2 \approx 0.6931$$, we have:  
$$
1.5556 \ln 2 \approx 1.5556 \times 0.6931 \approx 1.0778.
$$  
Thus,  
$$
2^{1.5556} \approx e^{1.0778} \approx 2.9387.
$$

Now compute the final population:  
$$
P(14) \approx 4800 \times 2.9387 \approx 14106.96.
$$

Rounding to the nearest whole number, the population is approximately  
$$
\boxed{14107}.
$$
After 14 hours, the population of bacteria is approximately 14,107.

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Biology Questions