Question

The following equation represents the number of fish in a pond, F(x), after x number of weeks. F(x) = 500 (1.2)x. How many fish are in the pond after 4 weeks?

a. 600 fish
b. 1036 fish
c. 2000 fish
d. 2400 fish

How many fish are in the pond after 7 weeks?
a. 600 fish
b. 1036 fish
c. 1791 fish
d. 4200 fish

Answer 1

1) d. 2400

2) d.4200

Explanation:

As per given data:

F(x) represents number of fish

x represents number of weeks

Relation between F(x) and x is given as

F(x)= 500 (1.2)x

Now part 1:

How many fish are in the pond after 4 weeks=?

x=4

Putting in given equation F(x)= 500 (1.2)x

F(x)= 500(1.2)(4)

= 2400

Now part 2:

How many fish are in the pond after 7 weeks?

x=7

Putting in given equation F(x)= 500 (1.2)x

F(x)= 500(1.2)(7)

= 4200 !

Answer 2

Correct choice is b. 1036 fish.

and c. 1791 fish.

Explanation:

Given equation is
`f(x)=500(1.2)^x`.

There x represents number of weeks. We need to find about wow many fish are in the pond after 4 weeks.

To find that we will plug x=4 into above formula and simplify

`f(x)=500(1.2)^x`

`f(x)=500(1.2)^(4)`

`f(x)=500(2.0736)`

`f(x)=1036.8`

Which is approx 1036

Hence correct choice is b. 1036 fish.

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We can repeat same process with x=7 for 2nd problem

`f(x)=500(1.2)^(7)=1791.5904`

Hence correct choice is c. 1791 fish.