1) a) Describe the characteristics of the graph of y = −4 log x.

b. Graph y = −4 log x using technology to check your predictions. Include a screen shot or sketch of your graph.

2. Describe at least three similarities and three differences between the functions y = 10x and y = log x.

3. A researcher has determined that an equation that models the height of a particular species of tree is y = 20.2 log(x), where y is height in metres and x is time in years.

a. Graph the equation using technology.

b. Predict the height of the tree after 30 years.

c. Predict how old the tree will be when it is 15 m tall.

d. Describe how the height of the tree changes as time increases. Be specific.

Item 1

Given function:

y = −4 log x

a. Characteristics of graph

The value of y is undefined when x ≥ 0, so the graph will exist only on the right side of origin on cartesian plane.

For any values of x > 0, the values of y are always negative since the coefficient outside the log is negative (-4).

b. Actual graph (using Desmos)

2.

Given functions:

y = 10x eq. 1

y = log x eq. 2

Similarities:

??Both equations have variables x and y.

??Both equations have a coefficient 10 (since log has base 10)

??Both equations are y in terms of x.

Differences:

??Eq. 1 can be solved by division/multiplication of values, while eq. 2 can be solved by converting it to its exponential form

??Eq. 1 is linear, eq. 2 is exponential

??Domain of eq. 1 is x = all real numbers, while domain of eq. 1 is x > 0.

3.

Given function:

y = 20.2 log(x)

a. Actual graph (using Desmos)

b. Height of tree after 30yrs.

y = 20.2 log(x)

y = 20.2 log(30)

y ≈ 29.84 meters

c. Age at height 15m

y = 20.2 log(x)

15 = 20.2 log(x)

15/20.2 = log(x)

x = 10^15/20.2

x = 5.53 years

c.

Based on the graph, the tree continuously grows with respect to time; but its growth rate slows down as it gets older.

Please see the attached file for the complete solution