a product costs $110 today. how much will the product cost in t days if the price is reduced by (a) $5 a day…
a product costs $110 today. how much will the product cost in t days if the price is reduced by (a) $5 a day (b) 4% a day
Answer
Explanation:
Step1: Identify the initial - value and the rate of change for part (a)
The initial price is $P_0 = 110$ and the daily reduction is $5$.
Step2: Form the formula for the price after $t$ days
The price $P(t)$ after $t$ days is given by $P(t)=110 - 5t$.
Step3: Identify the initial - value and the rate of change for part (b)
The initial price is $P_0 = 110$ and the daily percentage reduction is $4%=0.04$.
Step4: Form the formula for the price after $t$ days
The price $P(t)$ after $t$ days is given by the formula for exponential decay $P(t)=110(1 - 0.04)^t=110\times0.96^t$.
Answer:
(a) $110 - 5t$ (b) $110\times0.96^t$