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

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Full solution

Q. For the function f f , f(0)=86 f(0) = 86 , and for each increase in x x by 1 1 , the value of f(x) f(x) decreases by 80% 80\% . What is the value of f(2) f(2) ?
  1. Understand the problem: Understand the problem.\newlineWe are given that f(0)=86f(0) = 86, which means when x=0x = 0, the value of the function ff is 8686. We are also told that for each increase in xx by 11, the value of f(x)f(x) decreases by 8080%. We need to find the value of f(2)f(2).
  2. Calculate f(1)f(1): Calculate the value of f(1)f(1).\newlineSince the value of f(x)f(x) decreases by 80%80\% for each increase in xx by 11, we need to find 80%80\% of f(0)f(0) and subtract it from f(0)f(0) to get f(1)f(1).\newline80%80\% of f(1)f(1)11 is f(1)f(1)22.\newlineSo, f(1)f(1)33.
  3. Calculate f(2)f(2): Calculate the value of f(2)f(2). Now, we need to decrease the value of f(1)f(1) by 80%80\% to find f(2)f(2). 80%80\% of 17.217.2 is 0.80×17.2=13.760.80 \times 17.2 = 13.76. So, f(2)=f(1)−(0.80×f(1))=17.2−13.76=3.44f(2) = f(1) - (0.80 \times f(1)) = 17.2 - 13.76 = 3.44.

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