Amy purchased a brand–new mountain bike, which she's riding through the winding trails. The bike's displacement is given by s(t) = t3 − 2t2 + 3. What is the bike's acceleration after three minutes?

a = 14 m/min²

Step-by-step explanation:

The displacement of bike is given by :

Velocity,

Finding velocity of the bike.

Acceleration,

At t = 3 minutes,

a = 6(3) - 4

= 18-4

= 14 m/min²

So, the bike's acceleration after 3 minutes is 14 m/min².

A) No, because it has a constant rate of change

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Explanation:

Each time x goes up by 1, y drops by 2.

This means,

slope = rise/run

slope = (change in y)/(change in x)

slope = (y drops by 2)/(x goes up by 1)

slope = -2/1

slope = -2

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We can pick two points from the table to plug into the slope formula. I'll pick the first two rows

m = slope

m = (y2-y1)/(x2-x1)

m = (2-4)/(7-6)

m = -2/1

m = -2

If you tried every pair of rows possible for this table, you'll get the same slope each time. This is why the rate of change is constant.

This means the data is linear instead of nonlinear. Plotting the points leads to a single straight line going through all four points. See the diagram below. The graph was made with GeoGebra.

The equation of that red line is y = -2x+16 which is equivalent to 2x+y = 16.

In the graph, going from A to B has us go down 2 and to the right 1, which is one visual way of seeing the slope is -2/1 = -2.