Question

appc unit 1 test
name

1. let ( w(a) ) give the weight of a baby giraffe, in pounds, ( a ) months after birth. which expression can be used to find the average rate at which the giraffe gained weight between month 4 and month 7?

a) ( \frac{w(4) + w(7)}{2} )
b) ( \frac{w(3) - w(0)}{3} )
c) ( \frac{w(7) - w(4)}{7 - 4} )
d) ( \frac{w(7) - w(4)}{3} )

Explanation:

Step1: Recall average rate formula

The average rate of change of a function \( f(x) \) over the interval \([a, b]\) is given by \(\frac{f(b)-f(a)}{b - a}\). Here, the function is \( w(a) \) (weight as a function of months after birth), and we want the average rate between month \( 4 \) (so \( a = 4 \)) and month \( 7 \) (so \( b=7 \)).

Step2: Apply the formula

Substitute \( f(x)=w(a) \), \( a = 4 \), and \( b = 7 \) into the average rate of change formula. We get \(\frac{w(7)-w(4)}{7 - 4}\). Simplify the denominator: \( 7-4 = 3 \), so the expression is \(\frac{w(7)-w(4)}{3}\).

Answer:

D) \(\frac{w(7)-w(4)}{3}\)