the number of bacteria in a culture is given by the function ( n(t)=925 e^{0.15 t} ) where ( t ) is measured…

the number of bacteria in a culture is given by the function ( n(t)=925 e^{0.15 t} ) where ( t ) is measured in hours. (a) what is the relative rate of growth of this bacterium population? your answer is percent (b) what is the initial population of the culture (at ( t = 0 ))? your answer is (c) how many bacteria will the culture contain at time ( t = 5 )? your answer is

the number of bacteria in a culture is given by the function ( n(t)=925 e^{0.15 t} ) where ( t ) is measured in hours. (a) what is the relative rate of growth of this bacterium population? your answer is percent (b) what is the initial population of the culture (at ( t = 0 ))? your answer is (c) how many bacteria will the culture contain at time ( t = 5 )? your answer is

Answer

Explanation:

Step1: Find the relative rate of growth

The general form of an exponential growth function is (n(t)=n_0e^{rt}), where (r) is the relative rate of growth. Comparing (n(t) = 925e^{0.15t}) with (n(t)=n_0e^{rt}), we get (r = 0.15). To convert to a percentage, we multiply by (100): (0.15\times100=15%)

Step2: Find the initial population

When (t = 0), substitute into (n(t)=925e^{0.15t}) (n(0)=925e^{0.15\times0}) Since (e^{0}=1), then (n(0)=925\times1 = 925)

Step3: Find the population at (t = 5)

Substitute (t = 5) into (n(t)=925e^{0.15t}) (n(5)=925e^{0.15\times5}=925e^{0.75}) Using a calculator, (e^{0.75}\approx2.117) (n(5)=925\times2.117 = 1958.225\approx1958)

Answer:

(a) (15) (b) (925) (c) (1958)