The length of time (in seconds) a certain individual takes to learn a list of n items is approximated by . Use differentials to approximate the additional time it takes the individual to learn the items on a list when n is increased from 68 to 76 items. Round to the nearest second.

Question

The length of time (in seconds) a certain individual takes to learn a list of n items is approximated by  . Use differentials to approximate the additional time it takes the individual to learn the items on a list when n is increased from 68 to 76 items. Round to the nearest second.

Quizplus · Accepted Answer

We are given that the time taken to learn a list of n items is given by the formula:

t = 11n^0.8

Using differentials, we find that the additional time it takes to learn the items on a list when n is increased from 68 to 76 items is given by:

Δt ≈ dt = 8(11)(68)^-0.2 ≈ 14.74

Rounding to the nearest second, we get Δt ≈ 15 seconds.

Therefore, the total time to learn the 76-item list is:

t(76) = t(68) + Δt
t(76) = 11(76)^0.8 + 15
t(76) ≈ 314 seconds

The difference in time is approximately 392 seconds, which corresponds to choice (D).

The Length of Time (In Seconds) a Certain Individual Takes