Question

e. i can explain what a growth factor means in a situation.
for each problem (in full sentences)

• state the growth factor and its meaning in context
• state the initial value and its meaning in context

a. jimmy takes 400 mg of advil. it decreases at a rate of 4% out of his body.
1 - 0.04 = 0.96 this means jimmy still has 96% of advil left
initial value is 400mg and thats how much advil was in his body

b. tara bought a car for $50,000 dollars. it decreases in value by 13% each year.
1 - 0.13 = 0.87

Explanation:

Part a:

Step1: Identify Growth Factor

The decay rate is 4% or 0.04. For exponential decay, the growth (decay) factor is $1 - r$, where $r$ is the rate. So, growth factor = $1 - 0.04 = 0.96$.

Step2: Interpret Growth Factor

The growth factor of 0.96 means that each hour (or time unit), the amount of Advil in Jimmy's body is 96% of the previous amount.

Step3: Identify Initial Value

The initial value is 400 mg. This is the amount of Advil Jimmy took initially (at time 0).

Step4: Interpret Initial Value

The initial value of 400 mg means that at the start (when Jimmy took the Advil), there was 400 mg of Advil in his body.

Part b:

Step1: Identify Growth Factor

The decay rate is 13% or 0.13. The growth (decay) factor is $1 - r = 1 - 0.13 = 0.87$.

Step2: Interpret Growth Factor

The growth factor of 0.87 means that each year, the value of Tara's car is 87% of its value from the previous year.

Step3: Identify Initial Value

The initial value is $50,000. This is the value of the car when Tara bought it (at time 0, i.e., year 0).

Step4: Interpret Initial Value

The initial value of $50,000 means that when Tara purchased the car, its value was $50,000.

Answer:

s:

Part a:

• Growth Factor: 0.96. Meaning: Each time unit, the Advil amount is 96% of the previous amount.
• Initial Value: 400 mg. Meaning: Initial Advil amount in Jimmy's body.

Part b:

• Growth Factor: 0.87. Meaning: Each year, the car's value is 87% of the previous year's value.
• Initial Value: $50,000. Meaning: Initial value of the car when bought.