Question

The helght of a plant with an initial helght of 4.5 inches is recorded each week for 5 weeks. The data is used to find aline of best fit for the plant's height. The equation for the line is y = 1.8x + 4.5, where x is the number of weeks afterthe first week, and y is the height of the plant. The label on a plant nutrient supplement claims that customers who usethe supplement will see their plants grow at a rate that is more than twice their growth rate without any supplementWhich of the following could have been the equation for the line of best fit for the plant's helght if the nutrientsupplement had been used on the plant? SELECT ALL THAT APPLY A)y = 0.9x + 4.5B)y = 2.0x + 4.5C)y = 2.0x + 6.7D)y = 3.6x + 9.0E)y = 3.8x + 4.5F)y = 4.0x + 4.5G)y = 4.0x + 6.7H)y = 4.5x + 4.5

Answer 1

$\begin{gathered} E)y=3.8x+4.5 \\ F)\text{ y=4.0x+4.5} \\ H)y=4.5x+4.5 \end{gathered}$

Explanation

Step 1

Let

$\begin{gathered} y=f(x) \\ f(x)=1.8x+4.5 \\ y=1.8x+4.5 \end{gathered}$

customers who use the supplement will see their plants grow at a rate that is more than twice their growth rate without any supplement.

the initial height of the plant is the same = 4-5 inches

the rate of change is more than 2 = minimun 2*1.8=minimum =3.6 minimum.

Hence

$F(x)=2\cdot f(x)$

$\begin{gathered} y=3.6x+\text{4. }5 \\ E)y=3.8x+4.5 \end{gathered}$

if you strictly choice all the rate than is more than twice, you got

$\begin{gathered} E)\text{ because 3.8 is two or more times 1.8 and 4.5 is the initial heigth} \\ F)\text{ because 40 is two or more times 1.8 and 4.5 is the initial heigth} \\ H)\text{ because 4.5 is two or more times 1.8 and 4.5 is the initial heigth} \end{gathered}$