Question

The weight of an elephant is 40 pounds. Five years later, the elephant's weight has grown to 70 pounds. The elephant's weight always increases, but never exceeds 95 pounds.

Assume that the elephant's weight is a linear-to-linear rational function of time. What will the elephant's weight be 23 years from now?

Answer 1

there is a horizontal asymptote at y=95
assuming (0,40) and (5,70) are on the curve,
y = (ax+b)/(cx+d)
where a/c = 95 and b/d = 40
y = (95x+40)/(x+d)
solving y(5)=70 we get

y = (95x + 500/3)/(x + 25/6)
or y = (570x+1000)/(6x+25)

now find y(23)

Answer 2

Thank you so much! I can take it on from here :)