**1. **The graph shows the average price of stock each year for 11 years.

Which statements are true?

**The price of the stock increased the first 3 years.**

**The price of the stock never fell below its original value.**

**The average price in year 11 was less than the relative maximum price between years 1 and 5.**

**The value of the stock is negative between the third year and midway between the eighth and ninth year.**

**The stock started to increase again between the eighth and ninth year.**

**2.** Consider two functions: g(x)=20(1.5)^{x} and the function f(x) shown in the graph.

Which statements are true?

**g(x) has a greater y-intercept than f(x).**

**f(x) and g(x) are negative when x is less than 0.**

**f(x) and g(x) are both increasing on the interval (−∞, ∞) .**

**f(x) increases at a faster rate than g(x)does on the interval (−5, −3) .**

jbouyer
Feb 13, 2018

#1**+3 **

**1.**

The price of the stock increased the first 3 years.

True

The price of the stock never fell below its original value.

True

The average price in year 11 was less than the relative maximum price between years 1 and 5.

False

The value of the stock is negative between the 3^{rd} year and midway between the 8^{th} and 9^{th} year.

False

The stock started to increase again between the 8^{th} and 9^{th} year.

True

hectictar
Feb 14, 2018

#2**+3 **

**2.**

And g(x) = 20(1.5)^{x}

g(x) has a greater y-intercept than f(x).

the y-intercept of g(x) = g(0) = 20(1.5)^{0} = 20

the y-intercept of f(x) = 15

20 is greater than 15 , so

True

f(x) and g(x) are negative when x is less than 0.

False – there are no values that cause f(x) or g(x) to be negative.

f(x) and g(x) are both increasing on the interval (−∞, ∞) .

True

f(x) increases at a faster rate than g(x) does on the interval (−5, −3) .

This is harder to tell....

rate of increase of f(x) on the interval looks like about 0.1

rate of increase of g(x) on the interval ≈ 1.646

so I think its

False

hectictar
Feb 14, 2018

#3**+3 **

I believe that hectictar's last answer is correct , as well

It appears that f(x) might be = 15(2)^x since the points (0, 15) and (1, 30) are on the graph

Rate of change on -3 to -5 for f(x) =

[ 15(2)^(-3) - 15 (2)^(-5) ] / [ -3 - - 5 ] = ( 15/8 - 15/32 ) / 2 ⇒ 0.703

Rate of change on -3 to - 5 for g(x)

[ 20(1.5)^(-3) - 20(1.5)^(-5) ] / [ - 3 - - 5 ] = (160/27 - 640/243 ) / 2 ⇒ 1.646

So....."False" seems correct

CPhill
Feb 14, 2018