After one full day, the view count is multiplied by a constant factor $r$, and then 2,000 is added. Write a recurrence for $V(d+1)$ in terms of $V(d)$.

Write $V(1)$, $V(2)$, and $V(3)$ from the recurrence. The added 2,000 terms form a geometric sum in powers of $r$.

In Desmos, define the daily multiplier:

r=(1.25)^(16)*(1.10)^(24)

Define a recursive sequence (Desmos supports sequences):

V(0)=800

V(n+1)=r*V(n)+2000

Evaluate the sequence for a few values (like $n=1,2,3$) and compare with the answer choices. The choice that matches all values is

$V(d)=800\left((1.25)^{16}(1.10)^{24}\right)^d+2000\cdot\frac{\left((1.25)^{16}(1.10)^{24}\right)^d-1}{(1.25)^{16}(1.10)^{24}-1}$. Аniko Qu⁠е‌ѕtio​n​ Вank

Each 12-hour block is $720$ minutes.

• First 12 hours: $720/45=16$ intervals, multiplier $(1.25)^{16}$.
• Second 12 hours: $720/30=24$ intervals, multiplier $(1.10)^{24}$.

So the multiplicative growth factor for one full day (before the ad) is

Let $V(d)$ be the number of views after $d$ full days. SАТ рre‌p by Аniкο.a‍i

At the end of each day, the views are multiplied by $r$, then 2,000 views are added:

with initial value $V(0)=800$.

Compute the first few terms to see the pattern:

V(d)=800r^d+2000\left(r^{d-1}+r^{d-2}+\cdots+1\right).

The sum $r^{d-1}+r^{d-2}+\cdots+1$ is a geometric series with $d$ terms, so

Substitute $r=(1.25)^{16}(1.10)^{24}$:

So the correct choice is $V(d)=800\left((1.25)^{16}(1.10)^{24}\right)^d+2000\cdot\frac{\left((1.25)^{16}(1.10)^{24}\right)^d-1}{(1.25)^{16}(1.10)^{24}-1}$.