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The population P(t) at the end of year t is ![P(t) = 25,000 \times (1.12)^t](https://tex.z-dn.net/?f=P%28t%29%20%20%20%3D%2025%2C000%20%5Ctimes%20%281.12%29%5Et)
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Step-by-step explanation:
The initial population of town of Madison = 25,000
The rate at which the population is increasing = 1.12 times
So, the increase in population first year :
( the initial population) x
= 1.12 x ( 25,000)
= 28,000
So, the population at the end of first year = 28,000
Similarly, the increase in population second year :
( the initial population) x (1.12)² = ( 25,000) x (1.12)²
= 31,360
So, the population at the end of second year =31,360
Now, to calculate the population in t years from now:
The population P(t) at the end of year t is
![P(t) = 25,000 \times (1.12)^t](https://tex.z-dn.net/?f=P%28t%29%20%20%20%3D%2025%2C000%20%5Ctimes%20%281.12%29%5Et)