Three years after purchase, the card’s value is $5. Over the three years after it was purchased, the card’s value increased by $5 every
year. Three years after purchase, the card’s value will increase by $5 over the next
year. 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. The instantaneous rate of
change of the card’s value with respect to time 3 years after purchase is $5 per year.

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Before watching the videos, think about and answer these questions to the best of your ability.

The function gives the value of a particular baseball card in dollars where is the
number of years since the card was purchased. It turns out that . Which statement
best explains the meaning of .

The images below show the graph of a logarithmic function given by . To the right is
an image zoomed in on the point . It turns out that .
After zooming enough to where the graph of appears essentially linear, which
statement best describes the length of the blue vertical vector?

The length of the
blue vector is . The length of the blue vector is . The length of the
blue vector is . The length of the blue vector is times as much as the
value of . The length of the blue vector is times as much as the value
of . The length of the blue vector is times as much as the value of .