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 values in the table and solve for a and b.
Using the first set of values (x=0, P(x)=14.7):
14.7 = a(b)^0
14.7 = a
Using the second set of values (x=1, P(x)=12.054):
12.054 = a(b)^1
12.054 = ab
So, we have two equations:
a = 14.7 .............(1)
ab = 12.054 ........(2)
From equation (1), we can substitute the value of a in equation (2):
14.7b = 12.054
Now, solve for b:
b = 12.054/14.7
b = 0.82 (approx)
Now, substitute the value of b in equation (1) to find a:
a = 14.7
Therefore, the expression for P(x) is:
P(x) = 14.7(0.82)^x