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

Answer:

$y = 4(3)^x$.

Step-by-step 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 = $3 \times 4 = 12$ dishes

Year 2 = $3 \times 12 = 36$ 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 $y = 4(3)^x$.

Answer 2

Answer:

f(x) = 4(3)^x

Step-by-step explanation: