Question

Determine whether the given situation is best described by a linear model or an exponential model. What function models the situation? The membership of an online club is tripling every day.At 0 days (the starting point) there was only one member.

Answer 1

In this problem

we have an exponential growth function of the form

`y=a(b^x)`

where

a is the initial value -----> a=1 (one member)

b is the base of the exponential function

substitute the value of a

`\begin{gathered} y=(1)(b^x) \\ y=b^x \end{gathered}`

Find out the value of b

we know that

The membership of an online club is tripling every day

that means

For x=1

the value of y=3

substitute

`\begin{gathered} 3=b^1 \\ b=3 \end{gathered}`

therefore

The exponential equation

`y=3^x`

Find out the rate

b=1+r

3=1+r

r=2

r=200%

therefore

The function that models the situation is

`y=3^x`

where

x is the number of days

y is the number of membership