Question

1. a persons post on tiktok went viral and the number of views tripled each hour. there were initially 15 views before it went viral.

a) does this situation represent linear or exponential growth? (circle one).
b) the person went to sleep after posting and woke up 5 hours later. how many views would they have? show your work below and be sure to answer in a full sentence! (3 pts)

Explanation:

Step1: Determine the type of growth

Since the number of views triples each hour, this is an exponential growth situation. The general formula for exponential growth is \(y = a\cdot b^{x}\), where \(a\) is the initial amount, \(b\) is the growth factor (\(b> 1\) for growth), and \(x\) is the time. Here, \(b = 3\) (tripling each hour).

Step2: Calculate the number of views after 5 hours

We know that the initial number of views \(a=15\), and the time \(x = 5\) hours. Using the formula \(y=a\cdot b^{x}\), we substitute \(a = 15\), \(b = 3\), and \(x = 5\) into the formula:

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Answer:

a) This situation represents exponential growth.

b) The person would have \(3645\) views. After posting, the number of views follows the exponential - growth formula \(y = 15\times3^{x}\), where \(x\) is the number of hours. When \(x = 5\) (5 hours later), \(y=15\times3^{5}=15\times243 = 3645\) views.