It's more difficult to breathe on top of a tall mountain than at sea level. This is because atmospheric pressure decreases at higher altitudes. This function models the atmospheric pressure, in pounds per square inch, x miles above sea level:
P(x)=a(b)x, where a and b are constants
This table shows two values of the function:
x P(x)
0 14.7
1 12.054
Find an expression for P(x). Write your answer in the form P(x)=a(b)x, where a and b are integers or decimals. Do not round.
P(x)=
To find the expression for P(x), we can use the given points from the table and substitute them into the equation P(x) = a(b)x.
First, substitute x = 0 and P(x) = 14.7:
14.7 = a(b)0
Since anything multiplied by 0 is 0, we have:
14.7 = a(0)
This means a(0) should equal 14.7. For this to be true, a must be any non-zero number. Let's choose a = 1.
Now, substitute x = 1 and P(x) = 12.054:
12.054 = a(b)1
12.054 = a(b)
We know a = 1, so we can substitute that in:
12.054 = 1(b)
12.054 = b
Therefore, the expression for P(x) = a(b)x, where a and b are integers or decimals, is:
P(x) = 1(12.054)x
Simplifying this gives us:
P(x) = 12.054x