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)?
Understand the Problem
The question is asking us to determine the value of the function f(x) at x = 2, given that the function's initial value at f(0) is 86 and it decreases by 80% for each increase of 1 in x.
Answer
The value of \( f(2) \) is \( 3.44 \).
Answer for screen readers
The value of ( f(2) ) is ( 3.44 ).
Steps to Solve
- Determine the rate of decrease in function value
The function decreases by 80% for each increase in ( x ) by 1. This means that only 20% of the function value remains after each increment.
- Calculate the function value at ( x = 1 )
Given ( f(0) = 86 ), and since the value decreases by 80%: [ f(1) = f(0) \times (1 - 0.80) = 86 \times 0.20 = 17.2 ]
- Calculate the function value at ( x = 2 )
Using the value of ( f(1) ): [ f(2) = f(1) \times (1 - 0.80) = 17.2 \times 0.20 = 3.44 ]
The value of ( f(2) ) is ( 3.44 ).
More Information
This function represents an exponential decay, where each increase by one results in retaining only a fraction (20%) of the previous value. Such a model is common in scenarios involving depreciation or certain natural processes.
Tips
- Forgetting to multiply by the remaining percentage instead of subtracting the percentage from the total.
- Confusing the order of operations when calculating subsequent values.
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