need help about exponential functions

[west yacht]

The initial population of District 41 stands at 10,000 individuals. District 41 experiences consistent annual growth at a rate of 10 percent. What will be the population of District 41 after a period of 4 years?

Answer: P = 10000(1.10)^t

Can someone help me explain how they got that formula?

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[tough gust]

So, imagine the first year of growing, then we should have 10,000*1.10 because that’s 110% of the starting population of 10,000.

In the second year we want a 10% increase from the first year, that is $(10,000 \cdot 1.10) \cdot 1.10$

[atomic aspen]

it becomes a power of 1.1

[tough gust]

Bro

[atomic aspen]

latex is weird man

[tough gust]

It’s okay

[midnight quail]

borekking

[tough gust]

It just assume it’s a comment

[atomic aspen]

yea

[tough gust]

In the thirst year we would have $\Bigl( (10,000 \cdot 1.10) \cdot 1.10 \Bigr) \cdot 1.10$

[midnight quail]

borekking

[tough gust]

So, After $t$ years we multiply by $1.10$ $t$ times, ei we multiply the starting value by $(1.10)^t$

[midnight quail]

borekking

[west yacht]

thanks, that makes a lot of sense