Question

Can someone double check my attached solution after the post to see if I correctly did the following problem?

Research by Meadows, Meadows, Randers and Behrens indicates that the earth has 3.2x10^9 acres of arable land available. The world population of 1950 required 10^9 acres to sustain it, and the population of 1980 required 2x10^9 acres. If the required acreage grows at a constant percentage rate, in what year will the population reach the maximum sustainable size?

Answer 1

above is the solution I got. Can someone make sure I didn't mess up

Answer 2

The value of t seems reasonable.

The question asks: what year will the population reach the maximum sustainable size?

So, would that be the year 2030, in mid-March?

Answer 3

wouldnt it be 2000???

Answer 4

I looked at it this way:

1950 --> 1 * 10^9

1980 --> 2 * 10^9

2010 --> 3 * 10^9

Year X --> 3.2x10^9

where X is 50.3 years after 1980.

Answer 5

If 30 years is the doubling time, I do not think the year 2000 seems correct.

Answer 6

your right, this is what I get for forgetting that 30 is the difference between 1980 and 1950. rookie mistake

Answer 7

thank you sir for responding, i think expon growth scares people lol

Answer 8

Exponential growth and decay is sometimes tricky. I am checking my text for the doubling formula now because I want to review some problems I did a year or so ago.

At this time of the day (night), the number of solvers here on OpenStudy is at a minimum. So, leave your question open if you like. The others can add their comments when they wake up or get back from class.