Title: Interpreting Derivatives PreVideo Questions
Course: Calculus Videos Project Modules

Q: The images below show the graph of a logarithmic function given by [Image: equation]. To the right is an image soomed in on the point [Image: equation]. It turns out that [Image: equation].
[Image: image]
After zooming enough to where the graph of [Image: equation] appears especially linear, which statement best describes the length of the blue vertical vector?
- The length of the blue vector is 4. (Incorrect)
- The length of the blue vector is [Image: equation]. (Incorrect)
- The length of the blue vector is 0.17. (Incorrect)
- The length of the blue vector is 0.17 times as much as the value of 4 (Incorrect)
- The length of the blue vector is 0.17 times as much as the value of [Image: equation]. (Correct)
- The length of the blue vector is 0.17 times as much as the value of [Image: equation]. (Incorrect)
A: The length of the blue vector is 0.17 times as much as the value of [Image: equation].

Q: The function [Image: equation] goves the value of a particular baseball card in dollars where [Image: equation] is the number of years since the card was purchased. It turns out that [Image: equation]. Which statement best explains the meaning of [Image: equation].
- Three years after purchase, the card's value is $5. (Incorrect)
- Over the three years after it was purchased, the card's value increased by $5 every year. (Incorrect)
- Three years after purchase, the card's value will increase by $5 over the next year (Incorrect)
- As time increases by a very small amount from 3 years, the card's value increases by 5 times as much as the change in time. (Incorrect)
- The instantaneous rate of change of the card's value with respect to time 3 years after purchase is $5 per year. (Correct)
A: The instantaneous rate of change of the card's value with respect to time 3 years after purchase is $5 per year.