Question

In a memory​ experiment, Alice is able to memorize words at a rate given by m '(t)= - 0.009t^2 + 0.6t. In the same memory​ experiment, Ben is able to memorize words at the rate given by M' (t)= - 0.003t^2 + 0.6 t.

1. Who has the higher rate of memorization?

a. Ben
b. Alice

2. How many more words does that person memorize from t = 0 to t = 10 (during the first 10 minutes of the experiment)?
3. Over the first 10 minutes of the experiment, on average, how many words per minute did Alice memorize?
4. Over the first 10 minutes of the experiment, on average, how many words per minute did Ben memorize?

Answer 1

1) Ben, 2)
`\Delta = 2`, 3)
`\dot m = 2.7`, 4)
`\dot M = 2.9`

Explanation:

1) Ben has a higher rate of memorization, since the coefficient of the second power is lesser than the one from Alice.

2) The number of words can be estimated by integrating the function:

Alice

`\Delta m = -0.003\cdot (10\,min)^(3) + 0.3\cdot (10\,min)^(2)`

`\Delta m = 27`

Ben

`\Delta M = -0.001\cdot (10\,min)^(3) + 0.3\cdot (10\,min)^(2)`

`\Delta M = 29`

`\Delta = \Delta M - \Delta m`

`\Delta = 2`

3) The average amount of words per minute is:

`\dot m = (27)/(10)`

`\dot m = 2.7`

4) The average amount of words per minute is:

`\dot M = (29)/(10)`

`\dot M = 2.9`