Question

on a website that sells funny t - shirts, the number of customers has been falling 10% per month. if the site had 14,000 customers this month, then how many should it expect to have 10 months from now? if necessary, round your answer to the nearest whole number.

Explanation:

Step1: Identify the formula for exponential decay

The formula for exponential decay is $N = N_0(1 - r)^t$, where $N_0$ is the initial amount, $r$ is the rate of decay, and $t$ is the time period.
Here, $N_0 = 14000$, $r = 0.10$ (since 10% = 0.10), and $t = 10$.

Step2: Substitute the values into the formula

Substitute the values into the formula: $N = 14000(1 - 0.10)^{10}$.
First, calculate $(1 - 0.10) = 0.90$. Then, we need to find $0.90^{10}$.
$0.90^{10}\approx0.3486784401$.

Step3: Calculate the final number of customers

Multiply this by the initial number of customers: $N = 14000\times0.3486784401$.
$14000\times0.3486784401 = 4881.4981614$.

Step4: Round to the nearest whole number

Rounding $4881.4981614$ to the nearest whole number gives $4881$.

Answer:

4881