how do I solve this word problem?

Question

The number of people involved in recycling in a community is modeled by the function n = 90sqrt(3t) + 400, where t is the number of months the recycling plant has been open.

a. find the number of people recycling when the plant has been open for 6 months.

b. find the month when about 670 people were recycling.

Answer 1

Hi Sydney,

 

n = 90sqrt(3t) + 400

 

a) when t = 6

n = 90√3*6 + 400

= 90√18 + 400

= 381 + 400 (90√18 = 381.8  I rounded it to 381 since you can not have decimal human count)

= 781

 

b) n = 670

670 = 90√3t + 400

270 = 90√3t

3 = √3t (take the square of both sides)

9 = 3t 

t = 3 months