SOLUTION: Amy is observing the population of the fish in a pond she built. She built the pond and populated it with 500 fish. The population of the fish doubles every year. Use x to repre

Question 1082986: Amy is observing the population of the fish in a pond she built. She built the pond and populated it with 500 fish. The population of the fish doubles every year. Use x to represent the number of years and y to represent the population of the fish. Which equation represents this situation? Need help Asap for Highschool!!!
Y=500(1.02)^x
Y=502^x
Y=500(2)^x
Y=2x

Found 2 solutions by Boreal, Theo:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
It is 500*(1+rate)^x
that is 500*(1+1)^x
y=500*(2)^x ANSWER
In one year there will be 1000, 500*2
in two years there will be 2^2*500=4*500=2000
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the number of fish in the pond starts with 500.

the population doubles every year.

this means that, every year, the number of fish in the pond is 2 times the number of fish that were in the pond the previous year.

so, at the end of the first year, there are 1000 fish in the pond.
at the end of the second year, there are 2000 fish in the pond.
at the end of the third year, there are 4000 fish in the pond.
at the end of the fourth year, there are 8000 fish in the pond.

1000 is equal to 2 * 500 which is equal to 2^1 * 500
2000 is equal to 2 * 2 * 500 which is equal to 2^2 * 500
4000 is equal to 2 * 2 * 2 * 500 which is equal to 2^3 * 500
8000 is equal to 2 * 2 * 2 * 2 * 500 which is equal to 2^4 * 500
in year x, therefore, the number of fish in the pond is equal to 2^x * 500.

that would be equal to selection 3, which is y = 500 * 2^x.

the general equation is f = p * (1 + r) ^ n

in your equation:

p = 500
r = 1

why is r = 1?

the growth rate is 100% each year.
500 * 2 = 1000 which means the growth is 500 which means the growth rate is equal to 500/500 = 1 * 100 = 100%.
1000 * 2 = 2000 which means the growth is 1000 which means the growth rate is equal to 1000/1000 = 1 * 100 = 100%

the formula becomes f = 500 * (1 + 1) ^ n

simplify and the formula becomes f = 500 * 2 ^ n

replace f with y and n with x and the formula becomes y = 500 * 2^x

that's your third selection.

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