Learning Objectives
- Use an exponential model (when appropriate) to describe the relationship between two quantitative variables. Interpret the model in context.
Let’s summarize what we have learned about exponential growth models:
The general form of an exponential growth model is y = C · bx.
- C is the initial value. It is the y-value when x = 0. It is also the y-intercept.
- b is the growth factor; it will always be greater than 1 in cases of growth. From the growth factor, we can determine the percentage increase in y for each additional 1 unit increase in x.
Let’s compare the general form of an exponential growth model to the general form for a linear model: y = a + bx.
- In the linear model, a is the initial value. It is the y-value when x = 0. It is also the y-intercept.
- b is the slope. From the slope, we can determine the amount and direction the y-value changes for each additional 1 unit increase in x.
Now we apply what we have learned about exponential growth to find a model for a set of data.
In this activity, you use a simulation to find an exponential model that fits the population growth of Kenya.
Here are the data graphed in the scatterplot in the simulation.
![Data on Kenya's population growth, from 1950–2010, in 10 year increments](https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/1729/2017/04/15031957/m4_non_linear_models_ExponentialRelationships1of2_image24.png)
Notice that the Kenyan population growth has a strong positive exponential form. Use the sliders in the simulation to adjust the values of C and b to find a reasonable exponential model that fits this data.
Click here to open this simulation in its own window.
Learn By Doing