1 of 8 0-day streak

Model and interpret a contextual rate of change

Question 1 of 8

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Separate the quantity value from its signed rate of change

The usable output mass Y grams during a process follows this model in t minutes. It is valid only on the stated interval

Y(t)=-\frac{1}{2}t^{2}-t+99

0\le t\le 4,\qquad t_0=3

(a)1 mark

Select the correct one-variable quantity model

Y(t)=-\frac{1}{2}t^{2}-t+99

Y(t)=-t-1

Y(t)=-t^{2}-2t+198

Y(t)=-\frac{1}{2}t^{2}-t+100

(b)2 marks

Enter every coefficient in descending powers, including zero for an absent term

Y'(t)=A_1t+A_0

\(\text{coefficient of }t\) \(\text{constant coefficient}\)

Enter the exact signed rate of usable output mass with respect to t at the stated input, in grams per minute

Signed instantaneous rate

(d)1 mark

Which statement correctly interprets the rate and its independent variable?

At this input, usable output mass is decreasing at 4 grams per minute

The rate is -4 minutes per gram

The rate equals the quantity value 183/2 grams

The sign says the quantity is increasing