Question

The function describes the spread of a rumor among a group of people in an enclosed space. N represents the number of people who have heard the rumor, and t is measured in minutes since the rumor was started. Which of the following statements are true?Check all that apply.A.There are 299 people in the enclosed space.B.The rumor spreads at a constant rate of 0.36 people per minute.C.It will take approximately 14 minutes for 100 people to hear the rumor.D.Initially, only one person had heard the rumor.

Answer 1

The statements which are true about this exponential function include the following:

C. It will take approximately 14 minutes for 100 people to hear the rumor.

D. Initially, only one person had heard the rumor.

What is an exponential function?

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

f(x) = abˣ

Where:

• a represents the initial value.
• b represents the rate of change.

At the initial time (t₀), the value of t₀ is zero (0) and the number of people who heard the rumor is given by:

N(t) = 300/(1 + 299e^{-0.36t})

Substituting the initial time (t₀) into this exponential function, we have;

N(t₀) = 300/(1 + 299e^{-0.36t₀})

N(0) = 300/(1 + 299e^{-0.36 × 0})

N(0) = 300/(1 + 299e^{0})

N(0) = 300/(1 + 299)

N(0) = 300/300

N(0) = 1 person.

At t = 14, the number of people who heard the rumor is given by:

N(t₁₄) = 300/(1 + 299e^{-0.36t₁₄})

N(14) = 300/(1 + 299e^{-0.36 × 14})

N(14) = 300/(1 + 299e^{-5.04})

N(14) = 300/(1 + 299(0.00647374831))

N(14) = 100 people.

In conclusion, there are 300 people in the enclosed space rather than 299 people.

Read more on exponential function here: brainly.com/question/27866047

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