Question

a certain culture of the bacterium streptococcus a initially has 9 bacteria and is observed to double every 1.4 hours. (a) estimate the number of bacteria after 28 hours. (round your answer to the nearest whole number.) bacteria (b) after how many hours will the bacteria count reach 10,000? (round your answer to one decimal place.) t

Answer 1

The number of bacteria after 28 hours is 9437184. It will take 14.1 hours to reach 10000 bacteria.

a) estimate the number of bacteria after 28 hours.

N(t) = $9*2$^$\frac{28}{1.4}$

using the calculations

N(t) =$9 * 1048576$

N(t) = 9437184 bacteria in 28 hours.

b) after how many hours will the bacteria count reach 10,000?

$9*2^{(t/1.4)}$ = 10000

find t

$2^{(t/1.4)}$ = 10000/9

$2^{(t/1.4)}$ = 1111.1

Using nat logs,

$\frac{t}{1.4}$ln(2) = ln(1111.1)

$\frac{t}{1.4}$ = $\frac{ln(1111.1)}{In2}$

using calculations

$\frac{t}{1.4}$ = 10.1178

t = 10.1178 * 1.4

t = 14.1 hours to reach 10000 bacteria

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