Two hundred forty students attended the dedication ceremony of a new building on

Question

Two hundred forty students attended the dedication ceremony of a new building on a college campus. The president of the traditionally female college announced a new expansion program, which included plans to make the college coeducational. The number of students who learned of the new program t hr later is given by the function f(t) = 6000/1 + Be^-kt. If 480 students on campus had heard about the new program 2 hr after the ceremony, how many students had heard about the policy after 3 hr? (Round your answer to the nearest integer.)

Explanation / Answer

f(t)=6000/(1+Be-kt)

initially t =0

f(0)=240

6000/(1+Be-0) =240

6000/(1+B) =240

(1+B) =6000/240

1+B=25

B=24

f(t)=6000/(1+24e-kt)

after 2 hours f(t)= 480

6000/(1+24e-k2)=480

(1+24e-k2)=6000/480

(1+24e-k2)=12.5

(24e-2k)=11.5

e-2k=11.5/24

-2k=ln(11.5/24)

-2k=-0.7357

k=0.3678534

f(t)=6000/(1+24e-0.3678534t)

after 3 hours

f(3)=6000/(1+24e-0.3678534*3)

f(3)=6000/(1+ 24*0.3317)

f(3)=6000/8.96

f(3)=669.6

f(3)=670

after 3 hours 670 students heard

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