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.
[tex]c(m)=\frac{2}{3}\times (3^{\frac{m}{10}}-1)[/tex]
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.
[tex]363=\frac{2}{3}\times (3^{\frac{m}{10}}-1)[/tex]
Multiply 3/2 both sides.
[tex]363\times \frac{3}{2}=(3^{\frac{m}{10}}-1)[/tex]
[tex]242=3^{\frac{m}{10}}-1[/tex]
Add 1 on both sides.
[tex]243=3^{\frac{m}{10}}[/tex]
[tex]3^5=3^{\frac{m}{10}}[/tex]
On comparing both sides we get
[tex]5=\frac{m}{10}[/tex]
Multiply both sides by 10.
[tex]50=m[/tex]
Therefore, the total number of calls will 363 after 50 minutes since the start of the phone tree.
