Question

The number of people, n, who know a rumor can be modeled using the equation n(*)=20(2)*, where * is the number of days since Monday. (A) Explain why n(0)=20. What does this represent in terms of the situation modeled? (B) What is the value of n(-2)? What does represent in the situation modeled?

Answer 1

Using an exponential function, it is found that:

a) n(0) = 20 means that on Monday, 20 people knew about the rumor.

b) n(-2) = 5, it means that on the previous Saturday, 5 people knew about the rumor.

What is an exponential function?

It is modeled by:

$y = ab^x$

In which:

• a is the initial value.

• b is the rate of change.

In this problem, the function is:

$n(x) = 20(2)^x$

Item a:

Day 0 is referent to Monday, hence n(0) = 20 means that on Monday, 20 people knew about the rumor.

Item b:

$n(-2) = 20(2)^{-2} = 5$

Since Day 0 is referent to Monday, Day -2 is referent to the previous Saturday, when 5 people knew about the rumor.

More can be learned about exponential functions at https://brainly.com/question/25537936