Question

the number of bacteria in a culture is given by the function
\
(t) = 955e^{0.25t}\\
where \\(t\\) is measured in hours.
(a) what is the relative rate of growth of this bacterium population?
your answer is 25 percent
(b) what is the initial population of the culture (at t=0)?
your answer is 955
(c) how many bacteria will the culture contain at time t=5?

Explanation:

⚡ Using what you learned: exponential growth and decay_model growth

Step 1: Identify the given function

The population of bacteria is modeled by:

$$ n(t) = 955e^{0.25t} $$

Step 2: Evaluate the function at \( t = 5 \)

Substitute \( t = 5 \) into the function:

$$ n(5) = 955e^{0.25 \times 5} $$

$$ n(5) = 955e^{1.25} $$

Step 3: Calculate the numerical value

Using the value of \( e^{1.25} \approx 3.49034 \):

$$ n(5) \approx 955 \times 3.49034 \approx 3333.28 $$

Rounding to the nearest whole number (or entering the exact expression depending on system requirements):

$$ n(5) \approx 3333 $$

Answer:

3333 (or \( 955e^{1.25} \))