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.
To find the expression for P(x) we need to use the provided values from the table.
At x = 0, P(x) = 14.7. This gives us the equation:
14.7 = a(b)^0
Since any number raised to the power of 0 is equal to 1, we have:
14.7 = a(1) = a
So, a = 14.7.
Now, we can use the second value from the table to find b.
At x = 1, P(x) = 12.054. This gives us the equation:
12.054 = 14.7(b)^1 = 14.7b
Dividing both sides of the equation by 14.7:
12.054/14.7 = b
Simplifying the left side:
0.820204 = b
So, b is approximately 0.820204.
Therefore, the expression for P(x) is:
P(x) = 14.7(0.820204)^x