Question

For the function f, f (0) = 86, and for each increase in x by 1, the value of f (x) decreases by 80%. What is the value of f (2)?

Answer 1

`\Huge \boxed{\boxed{\bf{f(2) = 3.44}}}}`

Explanation:

To find the value of
`\tt{f(2)}`, we can use the given information about the function
`\tt{f}`. We know that
`\tt{f(0) = 86}`, and for each increase in
`\tt{x}` by 1, the value of
`\tt{f(x)}` decreases by 80%.

First, let's find the value of
`\tt{f(1)}`. Since the value of
`\tt{f(x)}` decreases by 80% for each increase in
`\tt{x}` by 1, we can calculate
`\tt{f(1)}` as follows:

• 
  `\tt{f(1) = f(0) * (1 - 0.80) }`

• 
  `\tt{f(1) = 86 * 0.20}`

• 
  `\tt{f(1) = 17.2}`

Now, we can find the value of
`\tt{f(2)}` using the same method:

• 
  `\tt{f(2) = f(1) * (1 - 0.80)}`

• 
  `\tt{f(2) = 17.2 * 0.20 = 3.44}`

• 
  `\tt{f(2) = 3.44}`

So, the value of
`\tt{f(2)}` is 3.44.

#BTH1

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Answer 2

f(2) = 3.44

Explanation:

You want the value of f(2) if f(0) = 86 and each increase of x by 1 decreases f(x) by 80%.

Exponential function

When the decrease is 80% from one value to the next, the multiplier is (1-0.80) = 0.2. This means we can write f(x) as ...

f(x) = 86·(0.2^x)

Using this, we can find f(2) to be ...

f(2) = 86·(0.2²) = 86·0.04

f(2) = 3.44

__

Additional comment

We could also write this as a recursive function:

f(0) = 86; f(n) = f(n-1) - 0.80·f(n-1) = 0.2f(n-1)

Then f(1) = 0.2(86) = 17.2; f(2) = 0.2(17.2) = 3.44

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