the latest rare disease, expy, has entered your math classroom of 30. the students affected by the disease is modeled by the logistic function , where p(t) represents the number of students that understand exponential functions and t is time in days. clearly label each answer part. a) how many students understand exponential functions initially? (3 points) show your initial set-up and give your final answer. each step does not need to be shown. b) how many students will understand exponential functions after 3 days? (3 points) show your initial set-up and give your final answer. each step does not need to be shown. c) how many days will it take for 24 students to understand exponential functions? (4 points, multiple-choice) f) t

Therefore the answer to when math classroom of 30. the students affected by the disease is modeled by the logistic function is first case : 6 , second case : 15.68 and third case : 5.18

What is function ?

A function is a particular relation that transfers every element in set A to exactly one element in set B. There cannot be an empty set in either A or B. For a specific input, a function defines a specific output.

Here ,

Given:

P(t) = [tex]\frac{180}{5 + 25e^{-0.45t} }[/tex]

First case :how many students understand exponential functions initially is

Where t is number of days

t=0

P(0)= [tex]\frac{180}{5 + 25e^{-0.45(0)} }[/tex]

P(0)=180/(25+5)

P(0)=6

Second case: how many students will understand exponential functions after 3 days

t=3

P(3)=[tex]\frac{180}{5 + 25e^{-0.45(3)} }[/tex]

P(3) ≈ 15.68

Third case: how many days will it take for 24 students to understand exponential functions

t=24

P(24)=[tex]\frac{180}{5 + 25e^{-0.45(24)} }[/tex]

P(24) ≈ 5.18

Therefore the answer to when math classroom of 30. the students affected by the disease is modeled by the logistic function is first case : 6 , second case : 15.68 and third case : 5.18

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