The question above is incomplete
Complete Question
A doctor estimates that a particular patient is losing bone density at a rate of 3% annually. The patient currently has a bone density of 1,500 kg/mg³. The doctor writes an exponential function to represent the situation. Which values should the doctor use for a and b in a function written in the form f(x) = ab^x, where f(x) represents the bone density after x years?
Answer:
a = 1500
b = 0.97
f(x) = ab^x
f(x) = 1500(0.97)^x
f(x) = 1500 × 0.97^x
Explanation:
We are to find a and b
This question has to do with exponential decay.
This is written as
y = a(1 - r)^x
f(x) = ab^x
r = rate of exponential decay
f(x) = y
a = a
b^x = (1 - r)^x
a = current bone density of the patient = 1500kg/m³
b = (1 - r)
r = 3% = 0.03
b = (1 - 0.03)
b = 0.97
Therefore,
a = 1500
b = 0.97
Hence:
f(x) = ab^x
f(x) = 1500(0.97)^x
f(x) = 1500 × 0.97^x