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 $f(x)=ab^{x}$, where $f(x)$ represents the bone density after $x$ years?
$a=\square$
$b=\square$

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 $100\% - 3\% = 97\%$. Convert this to a decimal: $b = 0.97$.

Answer:

$a = 1500$
$b = 0.97$