4. a function ( k(x) ) has an average rate of change equal to 7 on the interval ( 5leq xleq9 ). if ( k(5)=12…

4. a function ( k(x) ) has an average rate of change equal to 7 on the interval ( 5leq xleq9 ). if ( k(5)=12 ), then which of the following must be the value of ( k(9) )?\n(1) 28\n(2) 36\n(3) 40\n(4) 52

4. a function ( k(x) ) has an average rate of change equal to 7 on the interval ( 5leq xleq9 ). if ( k(5)=12 ), then which of the following must be the value of ( k(9) )?\n(1) 28\n(2) 36\n(3) 40\n(4) 52

Answer

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function (y = k(x)) over the interval ([a,b]) is given by (\frac{k(b)-k(a)}{b - a}). Here, (a = 5), (b=9), and the average rate of change is (7), and (k(5)=12).

Step2: Substitute the values into the formula

We have (\frac{k(9)-k(5)}{9 - 5}=7). Substitute (k(5) = 12) into the equation: (\frac{k(9)-12}{4}=7).

Step3: Solve for (k(9))

Multiply both sides of the equation (\frac{k(9)-12}{4}=7) by (4): (k(9)-12=7\times4). Then (k(9)-12 = 28). Add (12) to both sides: (k(9)=28 + 12).

Answer:

(k(9)=40), so the answer is (3).