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Suppose it takes 4 hours for a certain strain of bacteria to reproduce by dividing in half. If 70 bacteria are present to begin with, the total number present after xxdays is
f(x)=70⋅64x
Find the total number present after 1, 2 and 3 days.
There will be bacteria present after 1day, after 2 days and after 3 days.
____________
secondly,
Find f−1for the function ff.
f(x)=4x2+4
f−1(x)=

Respuesta :

MrRoyal

Answer:

1 day: 4480

2 days: 8960

3 days: 13440

[tex]f^{-1}(x) = \sqrt{\frac{x -4}{4}}[/tex] ---- function inverse

Step-by-step explanation:

Given

[tex]f(x) = 70 \cdot 64x[/tex]

Solving (a): The amount present after 1 day.

Here, [tex]x =1[/tex]

So:

[tex]f(1) = 70 \cdot 64*1= 4480[/tex]

Solving (b): The amount present after 2 days.

Here, [tex]x =2[/tex]

So:

[tex]f(2) = 70 \cdot 64*2= 8960[/tex]

Solving (c): The amount present after 3 days.

Here, [tex]x = 3[/tex]

So:

[tex]f(3) = 70 \cdot 64*2= 13440[/tex]

Solving (d): The inverse function of:

[tex]f(x)= 4x^2 + 4[/tex]

Replace f(x) with y

[tex]y= 4x^2 + 4[/tex]

Swap x and y

[tex]x= 4y^2 + 4[/tex]

Rewrite as:

[tex]4y^2 = x -4[/tex]

Divide by 4

[tex]y^2 = \frac{x -4}{4}[/tex]

Take square roots

[tex]y = \sqrt{\frac{x -4}{4}}[/tex]

Replace y with function inverse

[tex]f^{-1}(x) = \sqrt{\frac{x -4}{4}}[/tex]

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