The function N(X) = 90(0.86)* + 69 can be used to predict the temperature of a cup of hot chocolate in degrees Fahrenheit after x minutes. What is the

approximate average rate of change of the temperature of the hot chocolate, in

degrees per minute, over the interval [0, 6]?

1.

-8.93

2.

-0.11

3.

0.11

4.

8.93

The  approximate average rate of change of the temperature of the hot chocolate, in  degrees per minute, over the interval [0, 6] is;

Option 1; -8.93

We are given the function;

N(x) = 90(0.86)ˣ + 69

We want to find the average rate of change over the interval (0, 6).

Thus;

N(0) = 90(0.86)⁰ + 69

N(0) = 90 + 69

N(0) = 159°

N(6) = 90(0.86)⁶ + 69

N(6) = 105.411°

Formula for rate of change is;

Rate of change = Δy/Δx

Thus; Rate of change = (159 - 105.411)/(0 - 6)

Rate of change = -8.93

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-8.93

Step-by-step explanation:

Given the function:

N(X) = 90(0.86)^x+ 69

X in the interval [0, 6]

For X = 0

N(0) = 90(0.86)^0 + 69

90 + 69 = 159

For X = 6

N(6) = 90(0.86)^6 + 69

90(0.404567235136) + 69

= 105.41105116224

Therefore, average change of change in temperature ;

(temp 2 - temp 1) / ( time 2 - time)

(105.41105116224 - 159) / (6 - 0)

= - 53.58894883776 / 6

= - 8.93149147296

= - 8.93

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.