What is the math definition for 'counterexample'? When is counterexample used?

1 answer:

7 0

A <u>counterexample</u> is something that proves a statement, or equation, wrong. A counterexample is used in math when someone creates a theorem, writes an equation, or creates a new rule and someone proves it to be false.

<u>For Example:</u>
Let's say that I said <em>an even number plus an odd number always equals an even number</em>. A counterexample of that would be 4 + 5 = 9, because 9 is odd, therefore proving the statement wrong.

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<h3>The function for Bruce’s elevation is $f(x)=1505(6)^x$ and because b=6 that is greater than 0, it is an exponential growth function.</h3>

Step-by-step explanation:

We have given initial Bruce’s elevation = 1,505 feet.

We know, the exponential function $f(x)=a(b)^x$ , where a is the initial value, b is the growth factor and x is the exponent represents time in hours.

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Therefore, initial value a=1505, growth factor b for exponential function $f(x)=a(b)^x$ is 6.

Now we can plug a=1505 and b=6 in $f(x)=a(b)^x$ , we get

$f(x)=1505(6)^x$

Also note, if b>0, it would be an exponential growth function.

<h3>Therefore, the function for Bruce’s elevation is $f(x)=1505(6)^x$ and because b=6 that is greater than 0, it is an exponential growth function.</h3>

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