Question 1

Given the graph of Chuck's journey (Image 1), what is the domain and range of the function describing his distance from home over time?

Accepted Answer

$$[8, 15]$$ for domain, $$[0, 60]$$ for range

Question 2

Based on the graph of Chuck's journey (Image 1), during which time interval is the distance from home decreasing?

Accepted Answer

From 14:00 to 15:00

Question 3

If Chuck started his journey at 8:30 am instead of 8:00 am, how would the graph change?

Accepted Answer

The entire graph would shift right by 0.5 hours.

Question 4

Suppose Chuck started his journey 10 miles from home. How would the graph change?

Accepted Answer

The entire graph would shift up by 10 units.

Question 5

Refer to the logarithmic model $$f(x) = 8.77 + 14.9 \ln(x)$$ for life span (Image 2). What is the estimated life span for people born in 1925?

Accepted Answer

$$57$$ years

Question 6

Using the graph in Image 2, for what value of $$x$$ does the estimated life span reach $$68$$ years?

Accepted Answer

$$x = 53.26$$

Question 7

If $$x is $$the number of years since 1900, in what year does the model predict the life span will reach $$68$$ years?

Accepted Answer

$$1953$$

Question 8

Given the function $$f(x) = 8.77 + 14.9 \ln(x)$$, set up the equation to solve for $$x$$ when the life span is $$68$$ years.

Accepted Answer

$$68 = 8.77 + 14.9 \ln(x)$$

Question 9

What does the point $$(53.26, 68)$$ represent in the context of the life span model?

Accepted Answer

53.26 years after 1900, the estimated life span is 68 years.

Question 10

If the function $$f(x) = 8.77 + 14.9 \ln(x) is $$concave down, what does this imply about the rate of increase in life span over time?

Accepted Answer

The life span increases, but at a decreasing rate.

Question 11

For the journey graph (Image 1), during which time interval is Chuck's distance from home constant?

Accepted Answer

From 09:00 to 14:00

Question 12

If the function $$f(x) = 8.77 + 14.9 \ln(x)$$ estimates life span, what is the domain of this function in the context of years since 1900?

Accepted Answer

$$x \u003e 0$$

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