Question

The number of bacteria in a culture is given by the function n(t) =950e^0.45t Where t is measured in hours A) what is the continuous 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 __ Round to the nearest bacteria

Answer 1

Answer:

a) The continuous rate of growth of this bacterium population is 45%

b) Initial population of culture at t = 0 is 950 bacteria

c) number of bacterial culture contain at t = 5 is 9013 bacteria

Step-by-step explanation:

The number of bacteria in a culture is given by

n(t) = 950$e^{0.45t}$

a) rate of growth is

Bacteria growth model N(t) = no$e^{rt}$

Where r is the growth rate

hence r = 0.45

              = 45%

b) Initial population of culture at t = 0

n(0) = 950$e^{0.45(0)}$

       = 950$e^{0}$

       = 950 bacteria

c) number of bacterial culture contain at t = 5

n(5) =  950$e^{0.45(5)}$

      = 950$e^{2.25}$

      = 9013.35

      = 9013 bacteria

Answer 2

Using the exponential function, it is found that:

a) 45 percent.

b) 950.

c) 9013 bacteria.

A exponential function is modeled by:

$n(t) = n(0)e^{kt}$

In which:

• n(0) is the initial value.
• k is the continuous rate of growth.

In this problem, the model is:

$n(t) = 950e^{0.45t}$

Hence, $k = 0.45, n(0) = 950$, and:

a) 45 percent.

b) 950.

Item c:

At t = 5, we have that:

$n(5) = 950e^{0.45(5)} = 9013$

So 9013 bacteria.

A similar problem is given at https://brainly.com/question/14773454