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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?

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Aliwohaish12
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!

Answer:

Function is [tex]f(x)=1500(0.97)^x[/tex], 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

Since, the exponential decay is given by [tex]f(x)=ab^x=a(1-r)^x[/tex].

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

[tex]f(x)=1500(1-0.03)^x[/tex]

i.e. [tex]f(x)=1500(0.97)^x[/tex]

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

Hence, the function representing the bone density is [tex]f(x)=1500(0.97)^x[/tex].

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