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 find the total views at the end of the first month, we can use the formula for compound growth:

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

Where:

• A = total amount of views after n months
• P = initial views (250)
• i = growth rate (0.50)
• n = number of months (1)

Thus,

$A = 250(1 + 0.50)^1 = 250(1.50) = 375$

Rounded to the nearest whole number, the total views are 375.

Using the same formula, we want to find n when A equals 100,000 views:

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

Dividing both sides by 250 gives:

$400 = (1.50)^n$

Taking the logarithm of both sides, we have:

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

Calculating this value:

$n hickapprox 15$

Thus, it will take approximately 15 months for the video to go viral.