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# Linear growth

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In 1970, the population was 94,000. By 1992, the population had grown to 161,000. Assuming linear growth, what will the population be in 2035?

Thank you :)

May 7, 2021

#1
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Let's call 1970 our zero point. We use that to determine our zero point.

If a linear equation is $$y = mx + b$$

Then for us, $$b=94,000$$

(Note that I made 1970 our zero point for convenience)

Now, what's the change in population size our zero point? Well it's gone from 94,000 to 161,000, and it took 22 years. So the difference between those two numbers is our rise and 22 years is our run.

$$161,000 - 94,000 \over 1992 - 1970$$

$${66,000 \over 22} = 3,000$$

Rise over run is slope, or m. So $$m = 3,000$$.

So our equation is $$y = 3,000x + 94,000$$, where x is the years since 1970.

2035 is 65 years after 1970:

$$y = 3,000 * 65 + 94,000 = 195,000 + 94,000 = 289,000$$

May 7, 2021
#2
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From 1970 to 1992 = 22 years

population grew   161000 - 94000 = 67000

this is   67000/22 = 3045.45 per year

From 1970 to 2035   is   65 years

65 years * 3045.45/yr =  197954.54 ~~197955        add this to the starting population of 94000= 291955   in 2035

May 7, 2021