Question

The rate of vocabulary memorization of the average student in a foreign language course is given by

dv

dt

=

20

t + 1

where t is the number of continuous hours of study,

0 < t ≤ 4,

and v is the number of words. How many words would the student memorize in 3 hours? (Round your answer to the nearest whole number.)

words

Answer 1

Answer:-

Given that:-

The rate of vocabulary memorizationof the average student in a foreign language course is given by

where t is the number of continuous hours of study, and is the number of words . We have to find number of words would be student memorize in 3 hours.

Thus we have to find the function  .Now integrate both side of the Equation 1, we have

Take u = t+1 in right side of the integral. Then we have dt=du and thus we get

where C is an arbitrary constant.

As at time t = 0 , one student memorize v =0 words, that means v(0)=0

which gives us

Thus we get

putting t=3 in the above equation we get

Therefore , in 3 hours one student can memorize 28 words.