Question

The Golden Years Senior Citizen Center uses a phone tree to announce when the center will be closed for poor weather. When each person receives a phone call, that person has a list of three more people to call. The function c approximates the total number of calls made after m minutes since the start of the phone tree. c(m) = 3/2 * (3 ^ (m/10) - 1) Approximately how many minutes will it take for the number of calls to reach 363?

Answer 1

Answer:

50 minutes

Step-by-step explanation:

Answer 2

Answer:

50 Minutes.

Step-by-step explanation:

The function c approximates the total number of calls made after m minutes since the start of the phone tree.

$c(m)=\frac{2}{3}\times (3^{\frac{m}{10}}-1)$

We need to find the number of minutes after which the total number of calls will 363.

Substitute c(m)=363 in the given function.

$363=\frac{2}{3}\times (3^{\frac{m}{10}}-1)$

Multiply 3/2 both sides.

$363\times \frac{3}{2}=(3^{\frac{m}{10}}-1)$

$242=3^{\frac{m}{10}}-1$

Add 1 on both sides.

$243=3^{\frac{m}{10}}$

$3^5=3^{\frac{m}{10}}$

On comparing both sides we get

$5=\frac{m}{10}$

Multiply both sides by 10.

$50=m$

Therefore, the total number of calls will 363 after 50 minutes since the start of the phone tree.