nate is culturing bacteria that have a growth rate of 10% per hour. if the current population is 12,800…

nate is culturing bacteria that have a growth rate of 10% per hour. if the current population is 12,800 bacteria, how many bacteria will there be in 8 hours? if necessary, round your answer to the nearest whole number. bacteria submit

nate is culturing bacteria that have a growth rate of 10% per hour. if the current population is 12,800 bacteria, how many bacteria will there be in 8 hours? if necessary, round your answer to the nearest whole number. bacteria submit

Answer

Explanation:

Step1: Recall the exponential growth formula

The formula for exponential growth is ( P(t) = P_0(1 + r)^t ), where ( P_0 ) is the initial population, ( r ) is the growth rate (as a decimal), ( t ) is the time, and ( P(t) ) is the population after time ( t ). Here, ( P_0 = 12800 ), ( r = 0.10 ) (since 10% = 0.10), and ( t = 8 ).

Step2: Substitute the values into the formula

Substitute the values into the formula: ( P(8) = 12800(1 + 0.10)^8 ). First, calculate ( (1 + 0.10)^8 ). ( 1.10^8 \approx 2.14358881 ).

Step3: Calculate the final population

Multiply the initial population by this factor: ( P(8) = 12800 \times 2.14358881 \approx 27437.936768 ).

Step4: Round to the nearest whole number

Rounding ( 27437.936768 ) to the nearest whole number gives ( 27438 ).

Answer:

27438