Question

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)=

Answer 1

Answer:

1 day: 4480

2 days: 8960

3 days: 13440

$f^{-1}(x) = \sqrt{\frac{x -4}{4}}$ ---- function inverse

Step-by-step explanation:

Given

$f(x) = 70 \cdot 64x$

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

Here, $x =1$

So:

$f(1) = 70 \cdot 64*1= 4480$

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

Here, $x =2$

So:

$f(2) = 70 \cdot 64*2= 8960$

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

Here, $x = 3$

So:

$f(3) = 70 \cdot 64*2= 13440$

Solving (d): The inverse function of:

$f(x)= 4x^2 + 4$

Replace f(x) with y

$y= 4x^2 + 4$

Swap x and y

$x= 4y^2 + 4$

Rewrite as:

$4y^2 = x -4$

Divide by 4

$y^2 = \frac{x -4}{4}$

Take square roots

$y = \sqrt{\frac{x -4}{4}}$

Replace y with function inverse

$f^{-1}(x) = \sqrt{\frac{x -4}{4}}$