The exponential graph below shows the number of views of a popular online video, that grows at a compound rate of 50% per month - NSC Technical Mathematics - Question 5 - 2024 - Paper 1

To calculate the total number of views at the end of the first year (12 months), we use the compound interest formula:

$A = P(1 + i)^n$

Where:

• $A$ is the total amount (views),
• $P$ is the initial amount (250 views),
• $i$ is the interest rate per period (0.50), and
• $n$ is the number of periods (12 months).

Substituting the values:

$A = 250(1 + 0.50)^{12}$

Evaluating this: $A ≈ 32,437$

Therefore, the total number of views at the end of the first year is approximately 32,437.

To find out how long it will take to reach 100,000 views, we again use the compound interest formula:

$A = P(1 + i)^n$

We set $A = 100,000$, $P = 250$, and $i = 0.50$. Solving for $n$:

$100000 = 250(1 + 0.50)^n$

Dividing both sides by 250:

$400 = (1.50)^n$

Taking the logarithm:

n = rac{ ext{log}(400)}{ ext{log}(1.50)}

Calculating this gives:

$n ≈ 15$

To the nearest month, it will take approximately 15 months for the video to go viral.