Which function has a maximum -value of 4 and a midline of ?
Given , which equation represents ?
A function is defined as , where . What is the value of ?
Consider the function . Is an even function? Justify your answer.
Write an equation for , the function that results after is shifted up 5 units.
Write an equation for , the inverse of .
Is an even function? Justify your answer.
Write an equation for , the function that results after is shifted up 5 units.
Write an equation for , the inverse of .
Taylor wants to open an investment account with the \ 12006.4 %6.35 %$ annual interest compounded continuously.
Write functions for and to represent the value of her investment with America's Bank and Barnyard Bank as a function of time, , in years.
Taylor would like to invest the \ 1200$ into one bank for ten years making no additional deposits and no withdrawals. With which bank will Taylor earn the most money? Justify your answer.
Taylor chooses to invest her money in Barnyard Bank. Algebraically determine how long, to the nearest tenth of a year, it will take her initial investment to triple assuming she makes no deposits or withdrawals.
Write functions for and to represent the value of her investment with America's Bank and Barnyard Bank as a function of time, , in years.
Determine with which bank Taylor will earn the most money after ten years and justify your answer.
Algebraically determine how long, to the nearest tenth of a year, it will take her initial investment to triple assuming she makes no deposits or withdrawals.
For which values of , rounded to the nearest hundredth, will ?
What is the inverse of the function ?
Which sketch could represent the function ?
A cup of coffee is left out on a countertop to cool. The table below represents the temperature, , in degrees Fahrenheit, of the coffee after it is left out for minutes.
Based on these data, write an exponential regression equation, , to model the temperature of the coffee. Round all values to the nearest thousandth.
Sarah is fighting a sinus infection. Her doctor prescribed a nasal spray and an antibiotic to fight the infection. The active ingredients, in milligrams, remaining in the bloodstream from the nasal spray, , and the antibiotic, , are modeled in the functions below, where is the time in hours since the medications were taken.
Determine which drug is made with a greater initial amount of active ingredient. Justify your answer.
Sarah's doctor told her to take both drugs at the same time. Determine algebraically the number of hours after taking the medications when both medications will have the same amount of active ingredient remaining in her bloodstream.