Question

Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 1100 bacteria selected from this population reached the size of 1257 bacteria in six hours. Find the hourly growth rate parameter
.Note: This is a continuous exponential growth model.
Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.

Answer 1

The hourly growth rate parameter is equal to 2.22%.

How to determine the hourly growth rate parameter?

In Mathematics, an exponential function simply refers to a mathematical function whose values are generated by a constant that is raised to the power of the argument.

Mathematically, an exponential function can be modeled by using this equation:

A(t) = ae^{kt}

Where:

• a represents the initial value.
• t represents time.
• k represents the rate of change or growth rate.

Based on the information provided, we have the following:

A(t) = 1100e^{6k}   .....equation 1.

A(6) = 1257      .....equation 2.

Equating the two equations, we have:

1100e^{6k} = 1257

e^{6k} = 1257/1100

e^{6k} = 1.1427

Taking the natural log (ln) of both sides of the equation, we have:

6k = ln(1.1427)

6k = 0.1334

Hourly growth rate, k = 0.1334/6

Hourly growth rate, k = 0.0222

As a percentage, we have:

Hourly growth rate, k = 0.0222 × 100

Hourly growth rate, k = 2.22%.

Read more on growth rate here: brainly.com/question/15864523

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