At the time of posting a video, a social media channel had 53 subscribers. Each day for five days after...

1. TRANSLATE the problem information

• Given information:
  • Initial subscribers at posting: 53
  • Growth pattern: "number of subscribers doubled from the number the previous day"
  • Need equation for total subscribers n after d days
• What "doubled from previous day" means: multiply by 2 each day

2. INFER the mathematical pattern

• This describes exponential growth, not linear growth
• Each day the number is multiplied by the same factor (2)
• Exponential functions have the form: \(\mathrm{n = ab^d}\)
  • \(\mathrm{a}\) = initial value when \(\mathrm{d = 0}\)
  • \(\mathrm{b}\) = growth factor applied each time period
  • \(\mathrm{d}\) = number of time periods

3. TRANSLATE the specific values

• Initial value: \(\mathrm{a = 53}\) (subscribers at posting)
• Growth factor: \(\mathrm{b = 2}\) (doubling means ×2)
• Time variable: \(\mathrm{d}\) = days after posting

4. Build the equation

• Substitute into exponential form: \(\mathrm{n = ab^d}\)
• \(\mathrm{n = 53(2)^d}\)

5. INFER why other choices are wrong

• Choice A: \(\mathrm{n = 1(53)^d}\) means 1 initial subscriber growing by factor of 53
• Choice C: \(\mathrm{n = 53(1/2)^d}\) means halving each day (decay)
• Choice D: \(\mathrm{n = 53 + d}\) means adding d subscribers each day (linear growth)

Answer: B. \(\mathrm{n = 53(2)^d}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "doubled from the number the previous day" and think about linear growth instead of exponential growth.

They might think: "If it doubles, that means it increases by 2 each day" or "doubling means adding the same amount."

This leads them to select Choice D (\(\mathrm{n = 53 + d}\)), treating this as linear growth where d subscribers are added each day.

Second Most Common Error:

Poor INFER reasoning about exponential structure: Students recognize it's exponential but get confused about which number should be the base and which should be the coefficient.

They might think: "The 53 grows exponentially, so 53 should be the base" rather than understanding that 53 is the starting amount and 2 is the growth factor.

This may lead them to select Choice A (\(\mathrm{n = 1(53)^d}\)).

The Bottom Line:

This problem tests whether students can distinguish between linear and exponential growth patterns, and correctly identify the components (initial value vs growth factor) in exponential situations.