Question

a doctor determines 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/m³. 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:

Explanation:

Step1: Identify initial value (a)

The initial bone density is given as the current value, so $a = 1500$.

Step2: Calculate decay factor (b)

Since bone density decreases by 3% annually, the remaining density each year is $100\% - 3\% = 97\%$, or $0.97$. Thus, $b = 0.97$.

Answer:

a = 1500
b = 0.97