Lúcia posted a video of her cat playing on the piano. She found that the following expression modeled the total number of people who had viewed her video t days after she posted it. 18*16^(0.0125 t) After how many days did the total number of people viewing the video double from the original number of people? (Round your answer to the nearest day.)

Question

Lúcia posted a video of her cat playing on the piano. She found that the following expression modeled the total number of people who had viewed her video  t days after she posted it.  18*16^(0.0125 t) After how many days did the total number of people viewing the video double from the original number of people? (Round your answer to the nearest day.)

Bytelearn · Accepted Answer

Denote original number of viewers: Let's denote the original number of people who viewed the video as V. According to the given expression, V = 18. We want to find the time t when the number of viewers is double the original number, which means we want to find t when the number of viewers is 2V = 2 * 18 = 36. The expression modeling the total number of people who have viewed the video t days after it was posted is:  18 * 16^(0.0125t)  We need to set this equal to 2V and solve for t.Set up equation for doubling viewers: Set up the equation to find when the number of viewers doubles:  36 = 18 * 16^(0.0125t)  Divide both sides by 18 to isolate the exponential term:  2 = 16^(0.0125t)Use logarithms to solve: To solve for t, we need to use logarithms. We can use the natural logarithm (ln) or the common logarithm (log). Let's use the natural logarithm:  ln(2) = ln(16^(0.0125t))  Using the property of logarithms that ln(a^b) = b * ln(a), we can rewrite the right side of the equation:  ln(2) = 0.0125t * ln(16)Calculate value of t: Now, we need to solve for t by dividing both sides of the equation by (0.0125 * ln(16)):  t = ln(2) / (0.0125 * ln(16))  Calculate the value of t using a calculator:  t ≈ ln(2) / (0.0125 * ln(16)) t ≈ 0.69314718056 / (0.0125 * 2.77258872224) t ≈ 0.69314718056 / 0.03465735903 t ≈ 20.0000000000Round answer to nearest day: Round the answer to the nearest day:  t ≈ 20 days

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