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 21 hours. how many bacteria would there be after 27 hours, to the nearest whole number?

Explanation:

Step1: Define exponential growth formula

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

Step2: Plug in given values

$N_0=640$, $t=27$, $d=21$. Substitute into formula:
$N(27) = 640 \times 2^{\frac{27}{21}}$

Step3: Simplify the exponent

Simplify $\frac{27}{21} = \frac{9}{7} \approx 1.2857$

Step4: Calculate the growth factor

$2^{1.2857} \approx 2.432$

Step5: Compute final population

$640 \times 2.432 \approx 1556.48$

Step6: Round to nearest whole number

Round 1556.48 to the nearest integer.

Answer:

1556