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2 years ago

12

A doctor estimates that a particular patient is losing bone density at a rate of 3% annually. The patient currently has a bone d

ensity 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?

2 answers:

Molodets [167]2 years ago

7 0

Hi there

exponential function to represent the situation
F (x) = ab^x
F (x)=1500× (1−0.03)^x
F (x)=1500× (0.97)^x...answer

Where b represents 0.97. ..answer

Good luck!

katovenus [111]2 years ago

6 0

Answer:

Function is $f(x)=1500(0.97)^x$ , where a= 1500 and b= 0.97

Step-by-step explanation:

We are given that,

The current bone density of the patient, a = 1500 kg per mg³

The rate of decrease in the bone density, r = 3% = 0.03

<em>Since, the exponential decay is given by $f(x)=ab^x=a(1-r)^x$ .</em>

So, the function representing the bone density after x years is,

$f(x)=1500(1-0.03)^x$

i.e. $f(x)=1500(0.97)^x$

Thus, the value of a= 1500 and b= 0.97.

Hence, the function representing the bone density is $f(x)=1500(0.97)^x$ .

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