A doctor estimates that a particular patient is losing bone density at a rate of 3% annuallythe form f(x)=ab^ x , where f(x) represents the bone density after x years ?

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?

a = 1500

b = 0.97

f(x) = ab^x

f(x) = 1500(0.97)^x

f(x) = 1500 × 0.97^x

Step-by-step 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

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50