Word Translation Chapter 2 question 3

[rachelhong2012]

The population of grasshoppers doubles in a particular field every year. Approximately how many years will it take the population to grow from 2000 grasshoppers to 1000000 or more?

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The guide tells me to do it manually, I wonder if there's a short cut? Such as using exponential growth formula.

Thanks!

[mithunsam]

Let us see...

For number of grass coppers in nth year, you can write An = 2^n * 2000

If you are not clear, see below
A0 = 2000
A1 = 2 * 2000
A2 = 2^2 * 2000
- - -
An = 2^n * 2000

Question says
An > 1000000
=>2^n * 2000 > 1000000
=>2^n > 500

But we know 2^8 = 256 and 2^9 = 512

So, 9 is the answer

[jnelson0612]

Very nice! Thank you.