# St Pauls University Exponential Growth Model Discussion

Answer the following questions :

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: ?

When is the association negative in an exponential growth model?

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!”

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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.