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?

Answer 1

it is 1500 and .97 on

Explanation:

Answer 2

a = 1500 (initial Bone density)

b = 0.97 (remaining percentage every year)

x = x (years)

Step-by-step explanation:

The question already sets x as the "years" variable, and the function must be expressed:

`f(x) = a*b^x`

Then we can set a as the initial bone density: 1,500 kg/mg3

and b as the remaining percentage after each year: 100% - 3% = 97%

In decimal notation: 97% is equivalent to 0.97

The x exponent of b represents the succesive density reduction each year.

For example, replacing for values for the first 5 years we obtain the following results:

(Note: results are limited and rounded to two decimals)

`f(x) = 1500*0.97^1 = 1455`

`f(x) = 1500*0.97^2 = 1411.35`

`f(x) = 1500*0.97^3 = 1369,01`

`f(x) = 1500*0.97^4 = 1327,94`

`f(x) = 1500*0.97^5 = 1288,10`