Question

please help me. It’s due tomorrow morning

Answer 1

(A)

Step-by-step explanation:

To be able to compare the growth rates of these two people, we need to develop an equation to describe Ioana's growth history, just like Valentin did.

Let $P_1(5, 102)$ and $P_2(10, 127).$ Using the equation for the slope of a linear function,

$m = \dfrac{y_2 - y_1}{x_2 - x_1}$

and this will represent the growth rate for Ioana. The slope in Valentin's equation also represents the growth rate. Using the values of the points that we picked, we get

$m = \dfrac{127 - 102}{10 - 5} = \dfrac{25}{5} = 5$

The slope-intercept form of the equation that describes Ioana's growth can be written as

$h_I = 5(a - 5) + b$

Note that we used (a - 5) instead of the usual variable a because the twins started recording their heights at the age of a = 5. Next, we need to figure out b, essentially Ioana's height at age 5. From the table, we can see that that b = 102. Hence, the equation for Ioana's height is

$h_I = 5(a - 5) + 102$

Let's compare this with Valentin's equation for his height:

$h_V = 4.5(a - 5) + 104$

We can see here that the slope for Ioana's equation is larger than Valentin's, which means that Ioana's growth rate is faster than that of Valentin, even though Valentin was taller when they first started.