SOLUTION: I don't know how to solve this and I can't find anything in my text for this...help please =/ The weight in kilograms,W, of a female African elephant at age t years is gi

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I don't know how to solve this and I can't find anything in my text for this...help please =/ The weight in kilograms,W, of a female African elephant at age t years is gi      Log On


   

Question 769221: I don't know how to solve this and I can't find anything in my text for this...help please =/



The weight in kilograms,W, of a female African elephant at age t years is given by W(t)=2600(1-0.51e^-0.075t). Estimate the age, to the nearest year, of an adult female African elephant weighing 1800 kilograms.
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
The weight in kilograms,W, of a female African elephant at age t years is given by W(t)=2600(1-0.51e^-0.075t). Estimate the age, to the nearest year, of an adult female African elephant weighing 1800 kilograms.
Ans:
Substituting for Weight as 1800 in the equation, we get
1800+=+2600%2A%281+-+0.51%2Ae%5E%28-0.075t%29%29
Simplifying
%281+-+0.51%2Ae%5E%28-0.075t%29%29+=+1800%2F2600+=+9%2F13
0.51%2Ae%5E%28-0.075t%29+=+0.51%2F%28e%5E%280.075t%29%29+=+1+-+%289%2F13%29+=+0.3077
e%5E%280.075t%29+=+0.51%2F0.3077+=+1.6575
Taking natural logarithms of both sides
0.075%2At+=+ln%281.6575%29+=+0.5053
t+=+0.5053%2F0.075+=+6.737
So age of the elephant rounded off to nearest year is 7 years.

Hope you got it :)