Exponential and Logarithmic Functions - Remediation 1. Certain content on the internet can become viral when the content spreads exponentially. The spread of content published by a specific content creator can be modelled by the function N(t) = 145 x 1.25, where N is the number of people reached by the content, and t is the number of hours since the content's publication. (a) Write down the number of people reached immediately after the content's publication. [1] (b) Calculate the number of hours it takes for the content to reach 100 000 people. [2] (c) Calculate the number of people reached after 80 hours. [2] Approximately 5 billion people in the world are now connected to the internet. (d) Explain why the model starts to become unrealistic after about 3 days. [1] . .... ................ ................... ...... ....................... . .............. . . ... ................ ..... .......................2. The sound intensity level, D, in decibels (dB), can be modelled by the function D(I) = 10 log10(1) + 120, 1 2 0, where I is the sound intensity, in watts per square meter (W/m?). (a) A vacuum cleaner has a sound intensity of 1.6 x 10-5 W/m2. Calculate the intensity level of the vacuum cleaner. [2] (b) A fire truck siren has an intensity level of 124 dB. Find the sound intensity of the siren. [2] ........ ..............: ..... .................... ..................... .............................. ........................... ...................... ................. ..... ................ ..... .................. .............. ..... .. ................3. An oil tank at a mine site was at full capacity before the tank incurred a puncture in the base and the oil start to leak out. A site engineer used the following function, L(t), to model the percentage of oil remaining in the tank L(t) = 100e-kt, t20, where t is the number of days after the puncture occurred. The engineer found that after one day, 30% of the oil originally in the tank had leaked out. (a) Find the value of k. [2] (b) Use this model to find the percentage of oil remaining in the tank after 30 hours. [2] Based on the model, the engineer makes the claim that the tank will always have some oil in it and never completely empty. (c) State a mathematical reason supporting the engineers claim. [2] ........................... .............................. ...... ............... .................. ............................. ................................ .................4. The area, A, of a given square can be represented by the function A(P) = 16' P20, where P is the perimeter of the square. The graph of the function A, for 0