In a memory experiment, Alice is able to memorize words at a rate given by $m^{\prime}(t)=-0.009 t^{2}+0.6 t$. In the same memory experiment, Ben is able to memorize words at the rate given by $M^{\prime}(t)=-0.003 t^{2}+0.6 t$.
a) Who has the higher rate of memorization?
Alice
Ben
b) How many more words does that person memorize from $t=0$ to $t=10$ (during the first 10 minutes of the experime more words
(Simplify your answer.)
Therefore, Ben has the higher rate of memorization. The final answer is \(\boxed{Ben}\).
Step 1 :Given the rates of memorization for Alice and Ben as functions $m^{\prime}(t)=-0.009 t^{2}+0.6 t$ and $M^{\prime}(t)=-0.003 t^{2}+0.6 t$ respectively.
Step 2 :To determine who has the higher rate of memorization, we can compare the two rates by evaluating the functions at a specific time, say $t=1$.
Step 3 :Substitute $t=1$ into both functions, we get $m^{\prime}(1)=-0.009*1^{2}+0.6*1=0.591$ and $M^{\prime}(1)=-0.003*1^{2}+0.6*1=0.597$.
Step 4 :Comparing the results, we can see that at $t=1$, Ben (represented by $M^{\prime}(t)$) has a higher rate of memorization than Alice (represented by $m^{\prime}(t)$).
Step 5 :Therefore, Ben has the higher rate of memorization. The final answer is \(\boxed{Ben}\).