Respuesta :
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &27080\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=\textit{elapsed time}\dotfill &5\\ \end{cases} \\\\\\ A=27080(1+0.03)^5\implies A=27080(1.03)^5\implies A\approx 31393[/tex]
The user base of the new social media after 5 months will be 31,393.
What is compounding?
Compounding is a process where the interest is credited to the initial amount and interest, on the whole, is charged again. and this continues for t period of time.
It is given by the formula,
[tex]A = P(1+r)^n[/tex]
where, A is the value after t period of time, and,
r is the rate of interest.
As it is given that the user of the social media site is increasing by approximately 3% per month. Therefore, the user will be compounding per month. Thus, the user base after 5 months will be,
[tex]\text{Number of User} = \text{(Current user base)} \times (1+r)^t[/tex]
[tex]\text{Number of User} = 27,080 \times (1+0.03)^5[/tex]
[tex]\text{Number of User} = 27,080 \times (1+0.03)^5 = 31,393.1419 \approx 31,393[/tex]
Hence, the user base of the new social media after 5 months will be 31,393.
Learn more about Compounding:
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