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aefrain42
09.06.2020 •
Mathematics
If an exponential model was used to fit the data set below, which of the following would be the best prediction for the output of the model if the input was x=20?
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Ответ:
The equation is found to be:![y = 50.6e^{0.16x}](/tpl/images/0680/9123/79de5.png)
y(20) = 1241.34
Step-by-step explanation:
The given data is:
x: 3 7 11 14 17
y: 83 142 301 450 722
Now, we find sum summation values, relevant to the formula of exponential regression model, using calculator:
∑ ln y = 27.77305, ∑x ln y = 308.1494, ∑x = 52, ∑ x² = 664
and, n = no. of data points = 5
Now, we use formulae of exponential regression model to find out values of constant:
b = (n∑x lny - ∑x ∑ln y)/[n∑x² - (∑x)²]
b = [(5)(308.1494) - (52)(27.77305)]/[(5)(664) - (52)²]
b = 0.16
Now, for a;
a = (∑ln y - b∑x)/n
Therefore,
a = [(27.77305) - (0.16)(52)]/5
a = 3.9
For, α:
α = e^a = e^3.9
α = 50.6
So, the final equation of exponential regression model is given as:
Now, we find value of y for x = 20:
y(20) = (50.6) e^(0.16*20)
y(20) = 1241.34
Ответ:
1. A
2. B
3. B
4. C
Step-by-step explanation:
the words less than, greater than, less than equal to, and greater than equal to are key word you can use to solve this next time!