Question

aquaculture is the farming of fish and other aquatic animals. world aquaculture increased at a relatively constant rate from 1991-2001. in 1994 world aquaculture was about 20.8 million metric tons. in 2000 world aquaculture was about 33.5 million metric tons.

a) write an equation that gives world aquaculture (in millions of metric tons) as a function of the number of years since 1991.

b) in 2001 china was responsible for 70.2% of world aquaculture. approximate China's aquaculture in 2001.

Answer 1

anyone know how to do this?

Answer 2

This problem tells us that the rate at which aquaculture increased is relatively constant, which means that the increase per year is a constant number, and as a result the equation as a function of time is linear. We're asked to write the function as a function of years since 1991, so we'll let 1991 be t=0.

a). We know in 1994, at t=(1994-1991)=3, that aquaculture was 20.8 million tons. For simplicity, we'll use 20.8, remembering that the result we get from our equation will be in millions of tons. We also know that in 2000, at t = (2000-1991) = 9, aquaculture was at 33.5
From this we can get the slope: aquaculture increased by 33.5-20.8 = 12.7 over 9-3 = 6 years, so it's increasing at a rate of 12.7/6 = 2.1166666... million tons per year. For simplicity's sake, I'm going to write this as 127/60.

We can write the equation with just this information:
y = 20.8 + (t-3)*(127/60)

where y is millions of tons of produce. Note the (t-3) - we know that 20.8 million tons was produced at time t = 3 and that the slope is linear, so we can do this. We can also distribute the numbers to get:
y = 20.8 + (127/60)t - 6.35 = 14.45 + (127/60)t

b) For part b, we simply calculate the produce in 2001, then calculate China's share of it. t = (2001-1991) = 10
so
y = 14.45 + (127/60)*10 = 35.6166666... million tons.

China produced 70.2% of this total, so y(China) = 35.6166666 * 0.702 = 25.0029 million tons.

Answer 3

Thank you. I was way off from that.