# St Pauls University Exponential Growth Model Discussion

What is the general form of an exponential growth model?

Are all exponential models linear?

What is  in the general form for a linear model: ?

• What is  in the exponential model?
• When is the association negative in an exponential growth model?

• What do exponential models predict?
• Introduction to statistics.
This lab is worth 10 points. To earn full credit, you must complete step 1 and step 2.
Step 1: Answer all six questions below and be sure to explain your reasoning.
Step 2: Respond to a minimum of two other classmates. Critique their response and provide feedback.
Example of satisfactory response to classmates:
“John, I agree with your response to question 5. However, I would add that you should consider….”
Example of unsatisfactory response to classmates:
“John, great job!”

What is the general form of an exponential growth model?
Are all exponential models linear?
What is in the general form for a linear model: ?
What is in the exponential model?
When is the association negative in an exponential growth model?

What do exponential models predict?

Student 1 . Ana
The general form of the Exponential growth model is Y= C*b^x.
Where C is the initial value, and the y value when x=0. It is also the point where the line crosses
the y intercept.
B is the growth factor, or the decay factor. But b is always positive. It just depends on if b=less
or more than 1.
Exponential models are not all linear. They are in fact what we use when we find our data is
not supported by a linear shape.
The general form for the linear model is y= a + bx. Where a is the initial value and it is the y
value when X = 0. A is also where the line crosses the Y axis.
And b is the slope, or average, and we can determine the amount and direction the Y Value
changes for EACH additional 1 unit increase in X.
IN the exponential model we are given the initial value, C, and we are given the average
percentage increase/decrease/growth/decay with the b value. E.g., y=121(1.083)^x
121 is the amount they had on the first data reading, and we can tell the curve is positive
because b is above 1. And that we know the 1.083 is actually 108.3. the 100% being no change
from the year before, so 8.3% change in the years to come. We then put in how many years
forward we want to calculate, and put that number on the x. e.g., 4 years would look like,
Y=121(1.083)^4.
The negative association shows a decline/decay over the years. It is also when the b value =
less than 1. Eg, 0.76
Exponential models predict either the decay or growth in a graph beyond what our original
data tells us.
Student 2. emi
1. The general form of an exponential growth model is y=C x b^x.
2. Exponential models are best represented as non-linear models, as the pattern in the
residuals is more scattered when using a linear model.
3. The general form of a linear model is y=a+bx, where a represents the initial value or yintercept, b is the slope, and x is the independent variable.
4. In the exponential model, c is the value when x is equal to 0. B can be either the growth
factor or the decay factor and it is raised to a constant exponent.
5. When is the association negative in an exponential growth model? The association is
negative in an exponential growth model when b is greater than 0 and less than 1. This would
make b the decay factor and y would decrease.
6. Exponential models predict the growth or decay of a quantitative variable in the future by
multiplying by a constant.

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