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These two functions represent the growth of two different bacterial cultures in terms of the number of bacteria after x days.

f(x) = 2,000(2)^x (other one on the graph)

Answer the following:
A) Which function has the higher initial amount of bacteria? g(x) or f(x)
B) Which function has the greater amount of bacteria after two days? g(x) or f(x)

These two functions represent the growth of two different bacterial cultures in terms of the number of bacteria after x days fx 20002x other one on the graph An class=

Respuesta :

Answer:

A. The function f(x) has the higher initial amount of bacteria.

B. The function g(x) has the higher amount of bacteria after two days.

Step-by-step explanation:

The given function is

[tex]f(x)=2000(2)^x[/tex]

The graph of g(x) passing through the points (0,1000) and (1,3000). So the initial value is 1000 and the growth factor is 3.

The function g(x) is

[tex]g(x)=1000(3)^x[/tex]

Part A:

Substitute x=0, to find the initial blue of the functions.

[tex]f(0)=2000(2)^0=2000[/tex]

[tex]g(0)=1000(3)^0=1000[/tex]

Since 2000>1000, therefore the function f(x) has the higher initial amount of bacteria.

Part B:

Substitute x=2, to find the amount of bacteria after two days.

[tex]f(2)=2000(2)^2=8000[/tex]

[tex]g(2)=1000(3)^2=9000[/tex]

Since 8000<9000, therefore the function g(x) has the higher amount of bacteria after two days.

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