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A social media website had 100,000 followers its first year. The number of followers increased by 9% each year. Write an exponential growth function to represent this situation

Respuesta :

absor201

Answer:

an exponential growth function to represent this situation is:

[tex]x\left(t\right)=100,000\times \left(1.09\right)^t\:[/tex]

Step-by-step explanation:

We know that the exponential growth function is of the form

[tex]x\left(t\right)\:=\:x_0\:\times \:\left(1\:+\:r\right)^t[/tex]

where

  • x(t) represents the value at time t
  • x₀ represents the initial value at time t = 0. In other words, it is the initial value (the amount before measuring growth or decay)
  • r represents the growth factor when r > 0 and decay factor when r < 0
  • t represents the of time intervals that have passed

In our case,

Given that

A social media website had 100,000 followers its first year. Thus,

  • x₀  = 100,000

The number of followers increased by 9% each year. Thus,

  • r = 9% = 0.09

Thus, substituting r = 0.09 and x₀  = 100,000 in the growth function

[tex]x\left(t\right)\:=\:x_0\:\times \:\left(1\:+\:r\right)^t[/tex]

[tex]x\left(t\right)=100,000\times \left(1+0.09\right)^t\:[/tex]

[tex]x\left(t\right)=100,000\times \left(1.09\right)^t\:[/tex]

Therefore, an exponential growth function to represent this situation is:

[tex]x\left(t\right)=100,000\times \left(1.09\right)^t\:[/tex]