Question

A subscription-based website sends out email reminders to 15,000 customers whose subscriptions are due to be renewed, inviting them to renew at a discount. After the email is sent, the number of customers whose subscriptions are due to be renewed decreases at a rate that compounds hourly, for a per-day decrease of 14.4%. The number of such customers after n days is given by the expression below.
What does (1-0.144/24) represent?



A.
the decay rate, which reveals the hourly rate of change in the number of customers whose subscriptions are due to be renewed
B.
the initial number of customers whose subscriptions are due to be renewed
C.
the number of customers whose subscriptions are still due to be renewed after one day
D.
the change per hour in the number of customers whose subscriptions are due to be renewed

Answer 1

Given that a subscription-based website sends out email reminders to 15,000 customers whose subscriptions are due to be renewed, inviting them to renew at a discount. After the email is sent, the number of customers whose subscriptions are due to be renewed decreases at a rate that compounds hourly, for a per-day decrease of 14.4%.

So the above situation can be modeled by decay formula

$A=P\left(1-\frac{r}{n}\right)^{\left(nt\right)}$

Where P=initial value = 15000

r= per day decrease rate = 14.4%=0.144

n=number of hours = 24

t= number of days

A= present value.

So we get equation:

$A=15000\left(1-\frac{0.144}{24}\right)^{\left(24t\right)}$

Now compare that with given expression:

given expression represents only the parenthesis part which is basically called growth/decay factor.

which best matches with choice A.

Hence final answer is:

A.

the decay rate, which reveals the hourly rate of change in the number of customers whose subscriptions are due to be renewed