Question

there is a population of 10,000 bacteria in a colony. if the number of bacteria doubles every 250 hours, what will the population be 780 hours from now?
_______ bacteria

Explanation:

Step1: Define exponential growth formula

The formula for doubling population is $P(t) = P_0 \times 2^{\frac{t}{T}}$, where $P_0=10000$ (initial population), $t=780$ (time elapsed), $T=250$ (doubling time).

Step2: Calculate the exponent

$\frac{t}{T} = \frac{780}{250} = 3.12$

Step3: Compute population value

$P(780) = 10000 \times 2^{3.12}$
First calculate $2^{3.12} \approx 2^{3} \times 2^{0.12} \approx 8 \times 1.087 = 8.696$
Then $P(780) \approx 10000 \times 8.696$

Answer:

86960 bacteria (rounded to nearest whole number, or ~87000 for approximate value)