The table gives the number of active Twitter users worldwide, semiannually from 2010 to 2016.

glamrockqueen7 2021-02-09 Answered

The table gives the number of active Twitter users worldwide, semiannually from 2010 to 2016. Years sinceJanuary 1, 2010Twitter user(millions)0303.52320.5494.02551.0684.52841.51015.03022.01385.53072.51676.03103.02046.5317

Use a calculator or computer to fit both an exponential function and a logistic function to these data. Graph the data points and both functions, and comment on the accuracy of the models.

 
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Expert Answer

Velsenw
Answered 2021-02-10 Author has 91 answers

Step 1 Using Desmos, first add a table. (click on "+" at the upper left) and add the numbers. It should look something like in this image:

x1y10300.5491681.510121382.516732043.523242554.528453025.530763106.5317

Step 2 Next, you can get the exponential model form y=a  ekx by typing in the next box below the one with the table: y1  a  ekx1 Using the output from Desmos, we can write the exponential model as follows: y=89.1544  e0.219711x
y1 abx1
R2=0.8627 e1
a=89.1544
b=1.24572

Step 3 You can get the logistic model form y= M1 + Aekx by typing: Undefined control sequence \rightarrowM Using the output from Desmos, we can write the logistic model as follows: y= 325.7641 + 8.75376  e0.892708z
y  M1 + Aekx1
R2=0.9988
e1
m=325.764
A=8.75376
k=0.892708

Step 4 The logistic model is more accurate because it has larger R2 value. You can also see this from the graph below: The exponential and the logistic models are represented by the red and blue color curves respectively. image

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