Ms. Brockman wants to take her class on a trip to either the nature center or the zoo. The nature center charges $4 per student,
plus $95 for a 1-hour naturalist program. The zoo charges $6 per student plus $75 for a 1-hour guided tour. Find the number of students where the two field trips would have the same cost.
1 answer:
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Substitute , so that
, and
which is separable as
Integrate both sides with respect to . For the integral on the left, first split into partial fractions:
Solve for :
Replace and solve for
:
Now use the given initial condition to solve for :
so that the particular solution is