Question

lesson 14.2 checkpoint
once you have completed the above problems and checked your solutions, complete the lesson checkpoint below.
complete the lesson reflection above the circling your current understanding of the learning goal.

1. determine if an exponential would be an appropriate model for the data shown in each scatter - plot. select one that applies.
2. a student is given $50 to invest. the following data shows the amount that the investment is worth over several years. three regressions are used to model the data set.

linear regression model
quadratic regression model
exponential regression model
based on the models given above, which model gives you the most reasonable estimate of the students investment over the past five years?

Explanation:

Step1: Analyze exponential - model suitability

Exponential models have a characteristic curved - growth or decay pattern. In scatter plots, if the data points show a rapid increase or decrease in a non - linear, curved fashion, an exponential model may be appropriate. For the scatter plots in question 1, visual inspection is needed. But generally, if the points seem to follow a curve that gets steeper or shallower in a non - linear way, the answer is yes; if they seem to follow a straight - line or a different pattern, the answer is no.

Step2: Evaluate investment models

For the investment problem in question 2, linear regression has a constant rate of change (a straight - line). Quadratic regression has a parabolic shape. Exponential regression has a rapid growth rate over time. In real - world investment scenarios where the value can grow at an increasing rate over time, an exponential model is often more suitable as it can capture compounding effects.

Answer:

1. (Answers depend on visual inspection of scatter plots. Without seeing the actual plots clearly, we can't give definite yes/no answers)
2. Exponential Regression Model