Question

question
in a lab experiment, 550 bacteria are placed in a petri dish. the conditions are such that the number of bacteria is able to double every 14 hours. how many bacteria would there be after 7 hours, to the nearest whole number?
answer

Explanation:

Step1: Define growth formula

The exponential growth formula for doubling is $N(t) = N_0 \times 2^{\frac{t}{T}}$, where $N_0=550$, $t=7$, $T=14$.

Step2: Substitute values into formula

$N(7) = 550 \times 2^{\frac{7}{14}}$

Step3: Simplify the exponent

$\frac{7}{14} = \frac{1}{2}$, so $N(7) = 550 \times 2^{\frac{1}{2}} = 550 \times \sqrt{2}$

Step4: Calculate and round

$\sqrt{2} \approx 1.4142$, so $550 \times 1.4142 \approx 777.81$, rounded to nearest whole number.

Answer:

778