1) Write an exponential function that passes through the points \((2, 12)\) and \((6, 192)\).
2) Write an exponential function that passes through the points \((3, 62.5)\) and \((6, 7812.5)\).
3) Write an exponential function that passes through the points \((-2, 36)\) and \((2, \frac{4}{9})\)
4) Write an exponential function that passes through the points \((-3, \frac{125}{4})\) and \((2, \frac{1}{100})\).
5) Write an exponential function to model the visual pattern below. How many smiley faces will be in Step 10?
Source: visualpatterns.org
6) A study is done in which the number of bacteria in a liquid culture is monitored over a period of several hours. Given the data below shows \(10\) observations that were made. Determine a model of best fit for the time versus number of bacteria in the culture.
6) A study is done in which the number of bacteria in a liquid culture is monitored over a period of several hours. Given the data below shows \(10\) observations that were made. Determine a model of best fit for the time versus number of bacteria in the culture.
Source: https://commons.bcit.ca/math/examples/food/logs_exponentials/index.html
7) At what time will the liquid culture contain a count of \(1,000,000\) bacteria? Round answer to the nearest tenth.
8) The data below shows the temperature of coffee at each time after 7:15 am. Determine a model of best fit for temperature of time versus coffee temperature.
7) At what time will the liquid culture contain a count of \(1,000,000\) bacteria? Round answer to the nearest tenth.
8) The data below shows the temperature of coffee at each time after 7:15 am. Determine a model of best fit for temperature of time versus coffee temperature.
9) What will the temperature of the coffee be at 7:45 am? Round answer to the nearest degree.
10) Using your model, in how many minutes will the coffee be perfect to sip? (Note the temperature units) Round answer to the nearest tenth.
11) In how many minutes will the coffee be cool and uninviting? Round your answer to the nearest tenth.
12) In how many minutes will the coffee mildly burn your tongue? Round your answer to the nearest tenth.
13) Create an exponential model for the concentration of DDT in trout found in Lake Michigan from the table below for the years since \(1970\).
Source: https://chemicalstatistician.wordpress.com/2013/03/24/inference-in-simple-linear-regression-with-logarithmic-transformation-an-illustration-with-exponential-decay-of-ddt-in-trout/
14) What will the predicted concentration level of DDT be in \(2020\) if the trend continues? Round answer to two decimal places.
15) Create an exponential model for the concentration level of caffeine in the bloodstream. What is the half life of caffeine according to the model? Round half life time to one decimal place.
14) What will the predicted concentration level of DDT be in \(2020\) if the trend continues? Round answer to two decimal places.
15) Create an exponential model for the concentration level of caffeine in the bloodstream. What is the half life of caffeine according to the model? Round half life time to one decimal place.
16) According to National Institute of Health the half life of caffeine is \(5.7\) hours. Looking at the data from Starbucks coffees below, create a half-life exponential model for amount of caffeine in a person's body after drinking a Venti and for a Grande on the same graph for the most popular coffee in our geographic area.
Source: https://www.caffeineinformer.com/the-complete-guide-to-starbucks-caffeine and
https://qz.com/195631/what-people-order-at-starbucks-around-the-united-states/
17) What will the amount of caffeine in mg be from each size drink in \(2\) hours? Round to the nearest mg.
18) How long will it take for the amount of caffeine to fall below \(250\) mg for each size drink? Round answers to the nearest tenth.
19) Looking at the data from Starbucks coffees below, create an exponential half life model for amount of caffeine in a person's body after drinking a Vanilla Sweet Cream Cold Brew Venti.
https://qz.com/195631/what-people-order-at-starbucks-around-the-united-states/
17) What will the amount of caffeine in mg be from each size drink in \(2\) hours? Round to the nearest mg.
18) How long will it take for the amount of caffeine to fall below \(250\) mg for each size drink? Round answers to the nearest tenth.
19) Looking at the data from Starbucks coffees below, create an exponential half life model for amount of caffeine in a person's body after drinking a Vanilla Sweet Cream Cold Brew Venti.
20) How long will it take for the amount of caffeine be below \(100\) mg? This is the recommended maximum amount of caffeine for a teenager on a daily basis. Round answer to the nearest tenth.
Source: https://www.caffeineinformer.com/the-complete-guide-to-starbucks-caffeine
Review
21) Simplify \(3^{-\frac{1}{5}}\cdot\left(\frac{1}{3}\right)^{-\frac{2}{5}}\)
22) Solve the equation \(81^{x+1} = 27^{2x+3}\)
23) Given \(g(x) = ax^2 + 24\), \(a\) is constant and \(g(4) = 8\). What is the value of \(g(-4)\)?
24) Solve the equation \(log_6\;(x - 9) + log_6\;x = 2\)
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