Question

in a lab experiment, 640 bacteria are placed in a petri dish. the conditions are such that the number of bacteria is able to double every 10 hours. how many bacteria would there be after 25 hours, to the nearest whole number?

Explanation:

Step1: Define exponential growth formula

The formula for exponential growth (doubling) is $N(t) = N_0 \times 2^{\frac{t}{T}}$, where $N_0$ is initial population, $t$ is time elapsed, $T$ is doubling time.

Step2: Identify given values

$N_0 = 640$, $t = 25$ hours, $T = 10$ hours

Step3: Substitute values into formula

$N(25) = 640 \times 2^{\frac{25}{10}} = 640 \times 2^{2.5}$

Step4: Calculate $2^{2.5}$

$2^{2.5} = 2^2 \times 2^{0.5} = 4 \times \sqrt{2} \approx 4 \times 1.4142 = 5.6568$

Step5: Compute final population

$N(25) \approx 640 \times 5.6568 = 3620.352$

Step6: Round to nearest whole number

Round $3620.352$ to the nearest integer.

Answer:

3620