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Bharat sent a chain letter to his friends, asking them to forward the letter to more friends. The relationship between the elapsed time ttt, in days, since Bharat sent the letter, and the number of people, P(t)P(t)P, left parenthesis, t, right parenthesis, who receive the email is modeled by the following function: P(t)=2401⋅(87)t1.75 Complete the following sentence about the rate of change in the group of people who receive the email. The group of people who receive the email gains \dfrac{1}{7} 7 1 ​ start fraction, 1, divided by, 7, end fraction of its size every days.

Sagot :

Using exponential function concepts, it is found that the correct sentence is:

  • The group of people who receive the email gains [tex]\dfrac{1}{7}[/tex] of its size every 1.75 days.

Exponential function:

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^{\frac{t}{n}}[/tex]

In which:

  • A(0) is the initial value.
  • r is the rate of increase, as a decimal.
  • n is the period it takes for the amount to increase by r.

In this problem, the equation is:

[tex]P(t) = 2401\left(\frac{8}{7}\right)^{\frac{t}{1.75}}[/tex]

Hence, the parameters are:

[tex]n = 1.75[/tex]

[tex]1 + r = \frac{8}{7}[/tex]

[tex]r = \frac{1}{7}[/tex]

Hence, considering the parameters, the correct sentence is:

  • The group of people who receive the email gains [tex]\dfrac{1}{7}[/tex] of its size every 1.75 days.

You can learn more about exponential functions at https://brainly.com/question/25537936

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Answer:

Every 1.75 days

Step-by-step explanation:

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