Question

Park rangers released 4 fish into the pond in year 0. Each year, there were three times as many fish as the year before. How many fish were there after x years ? Write a function to represent this senario

Answer 1

f(x) = 4(3)^x

Explanation:

Answer 2

`y = 4(3)^x`.

Explanation:

Year 0 = 4 fishes

Since we are given that Each year, there were three times as many fish as the year before.

So , Year 1 =
`3 * 4 = 12` dishes

Year 2 =
`3 * 12 = 36` fishes

And so on

So, we can use formula of exponential growth :
`y = ab^x`

where y is the number of fishes after x years

a is the initial amount

b is the growth factor

x is the number of years

a = 4

b = 3

Substitute the values in the formula :

`y = 4(3)^x`

To Check substitute x = 0

`y = 4(3)^0`

`y = 4`

Park rangers released 4 fish into the pond in year 0

To Check substitute x = 1

`y = 4(3)^1`

`y = 12`

Park rangers released 12 fish into the pond in year 1

Hence verified

Hence a function to represent this senario is
`y = 4(3)^x`.