Algebra word problem

Question

The number of students that hear a rumor on a small college campus t days after the rumor starts is modeled y the logistic function R(t)= 1000/1+B e ^kt. If 8 students initially heard the rumor and 117 students heard the rumor after 1 day…

What is the carrying capacity for the number of students that will hear the rumor? (This is 1000)

Find b (b=124)

This is where I need help is the last 2 parts

Find k in exact simplified form

How long will it take 992 students to hear the rumor?

Answer 1

8 students initially heard the rumor

8=1000/1+B

B=124

 

117 students heard the rumor after 1 day

117=1000/(1+124*e^k)

Solve for k

k =-2.7991

 

How long it will take for 992 students to hear the rumor

 

992=1000/(1+124*e^(-2.7991t))

Solve for t using log

 

t =3.44days