Question

Busby is a famous cat on a video-sharing app. The total number of likes for Busby's most popular video grows by 10% every month. The total number of likes for the video in m months from now will be 4000×1.1
m
. How many likes does Busby's video have right now?

Answer 1

how many likes did busby have one month ago

Answer 2

To determine the current number of likes for Busby's video, we need to understand how the likes grow over time.

We know that the likes for the video in \( m \) months from now is given by:

\[
\text{Likes in } m \text{ months} = 4000 \times 1.1^m
\]

Since the likes grow by 10% each month, we can express the current number of likes (let's call it \( L_0 \)) using the formula for compound growth. The relationship can be expressed as:

\[
L(m) = L_0 \times (1.1)^m
\]

where:
- \( L(m) \) is the number of likes after \( m \) months,
- \( L_0 \) is the current number of likes,
- \( 1.1^m \) is the growth factor over \( m \) months.

According to the given information:

\[
4000 \times 1.1^m = L_0 \times 1.1^m
\]

We can see that both sides have \( 1.1^m \). Assuming \( 1.1^m \) is not equal to zero, we can divide both sides by \( 1.1^m \):

\[
4000 = L_0
\]

Thus, the current number of likes for Busby's video is:

\[
\boxed{4000}
\]