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) = abx, where f(x) represents the bone density after x years? a = b =

Answer 1

Since you're starting off with a bone density of 1,500 kg/mg3, that should be your a value. Anything in the form of ab
`b^(x)` will be arranged as follows: Your a value is your starting value, whereas the b value is the rate at which your starting value will change every x years. In this case, that would mean that f(x)=1,500*
`0.97^x`. A=1,500 and B=0.97

Answer 2

a = 1500 and b = 0.97

Explanation:

A patient is losing bone density at a rate of 3% annually.

Present bone density of the bones is 1500 kg/mg³

Doctor writes an exponential function to represent the situation.

The exponential function will be f(x) =
`a(b)^(x)` which is an explicit formula for exponential sequence.

Here a = initial bone density of the patient

b = common ratio of the sequence formed in x years

x = time in years

Then the values of a and b in the formula will be

a = 1500

b = (1 - 0.03) = 0.97

and the function will be
`f(x)=1500(0.97)^(x)`

Therefore, a = 1500 and b = 0.97 will be the answer.