4. Exponential and Logarithmic

Model Fitting — Quiz

Test your understanding of model fitting with 5 practice questions.

Practice Questions

Question 1

A population of fish in a lake is observed to be decreasing. Initially, there were $5000$ fish, and after $3$ years, there are $4000$ fish. If the population follows an exponential decay model, which equation best represents the number of fish $P(t)$ after $t$ years?

Question 2

A new product's sales initially grow very quickly, but then the rate of growth slows down as the market becomes saturated. Which type of model would be most appropriate to describe the product's sales over time?

Question 3

The amount of a certain medication in a patient's bloodstream decreases by a constant percentage every hour. If the initial dose is $200$ mg and after $2$ hours, $128$ mg remains, what is the hourly decay rate?

Question 4

When comparing an exponential growth model $y = a \cdot b^x$ (where $b > 1$) and a linear model $y = mx + c$, which of the following statements is true about their long-term behavior as $x$ increases indefinitely?

Question 5

A scientist is studying the relationship between the concentration of a nutrient and the growth rate of a plant. They observe that as the nutrient concentration increases, the growth rate increases, but the effect diminishes at higher concentrations. Which type of model would best fit this data?