# calculus

posted by .

for 0<=t<=21 the rate of change of the number of blakc flies on a coastal island at time t days is modeled by R(t)=3sqrt(t)cos(t/3) flies per day. There are 500 flies on the island at the time t=0. To the nearest whole #, what is the max # of flies for 0<=t<=21?

• calculus -

R = 3√t cos(t/3)
R' = 3/2√t cos(t/3) - √t sin(t/3)
R' = 0 when

3/2√t cos(t/3) = √t sin(t/3)
3cos(t/3) = 2t sin(t/3)
3/2 cot(t/3) = t
t = 1.96, 9.88, 19.08

not sure how there are 500 flies at t=0. That doesn't fit R(t). Anyway, if that can be fixed, just plug in those values for t to get what you need.

• calculus -

wait..dont u hve to integrate it?

• calculus -

oops. yes. I misread the problem. Didn't see the "rate of change" phrase.

• calculus -

wait..so how would you integrate that equation..im hving trouble with tht..

• calculus -

Beats me. It doesn't use standard elementary functions. Are you studying numerical methods?

## Similar Questions

1. ### math

joshua is raising fruit flies for science project at the begining of the first day he had 4fruit flies his fruit flies double in number each day how many fruit flies does he have at the end of three days
2. ### number patterns

joshua is raising fruit flies for a science project.at the begining of the first day,he had 4 fruit flies,his fruit flies double in number each day.how many fruit flies does he have at the end of three days
3. ### calculus

for 0<=t<=21 the rate of change of the number of black flies on a coastal island at time t days is modeled by R(t)=3sqrt(t)cos(t/3) flies per day. There are 500 flies on the island at the time t=0. To the nearest whole #, what …
4. ### Differential Equation

for 0<=t<=21 the rate of change of the number of black flies on a coastal island at time t days is modeled by R(t)=3sqrt(t)cos(t/3) flies per day. There are 500 flies on the island at the time t=0. To the nearest whole #, what …
5. ### calculus

The number of Drosophila fruit flies in a controlled experiment assumes the following growth pattern when the food source is limited: N(t) = 120 1+11e−0.4t where t measured in days. A. How many fruit files were there in the beginning?
6. ### Precalculus(another)

A small plane takes off from island A and flies in a straight line for 12 kilometers. At the same time, a sailor sitting in a sailboat who is 5 miles from the island measures the angled by from island A to the sailboat and the plane …
7. ### Pre calc

A small plane takes off from island A and flies in a straight line for 12 kilometers. At the same time, a sailor sitting in a sailboat who is 5 miles from the island measures the angled by from island A to the sailboat and the plane …
8. ### math

A small plane takes off from island A and flies in a straight line for 12 kilometers. At the same time, a sailor sitting in a sailboat who is 5 miles from the island measures the angled by from island A to the sailboat and the plane …
9. ### Trig

A small plane takes off from island A and flies in a straight line for 12 kilometers. At the same time, a sailor sitting in a sailboat who is 5 miles from the island measures the angled by from island A to the sailboat and the plane …
10. ### Math, Pre-Calculus.

A postal airplane leaves lsland A and flies 91 miles to Island B. It drops off and picks up mail and flies 63 miles to lsland C. After unloading and loading A- mail, the plane returns to lsland A at an average rate of 300 miles per …

More Similar Questions