Use algebraic methods to solve the following equations for m. a. 51' = 17 e = :1 Preview b. 16(2.1)$ = 45 e = : Preview 0. 6 = 106(0.61)\" e = E Preview Box 1: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2A3, 5+4) Enter DNE for Does Not Exist, 00 for Innity Box 2: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 518, 2'3, 5+4) Enter DNE for Does Not Exist, 00 for Innity Box 3: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2A3, 5+4) Enter DNE for Does Not Exist, 00 for Innity A 10-inch sunflower is planted in a garden and the height of the sunflower increases exponentially, increasing by 15% per day. a. Write a function f that determines the height of the sunflower (in inches) in terms of the number of days t since it was planted. f (t) = Preview b. How many days after it was planted will the sunflower be 34 inches tall? days Preview c. How many days after it was planted will the sunflower be 184 inches tall? days Preview Box 1: Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c Be sure your variables match those in the question Box 2: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 213, 5+4) Enter DNE for Does Not Exist, oo for Infinity Box 3: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 213, 5+4) Enter DNE for Does Not Exist, oo for InfinityJack plants a magic beanstalk that is 3 feet tall. The height of the magic beanstalk increases exponentially, doubling each day. a. Write a function f that determines the height of the beanstalk (in feet) in terms of the number of days t since the beanstalk was planted. rm 2 : Preview b. If the moon is directly over the beanstalk, how many days after the beanstalk was planted would the beanstalk reach the moon? (The moon is 238,900 miles 'om the earth, and there are 5,280 feet in 1 mile.) : views Preview c. If the sun is directly over the beanstalk, how many days after the beanstalk was planted would the beanstalk reach the sun? (The sun is 92,960,000 miles from the earth, and there are 5,280 feet in 1 mile.) E irvr Preview Box 1: Enter your answer as an expression. Example: 3x\"2+1, x/5, (a+b)/c Be sure your variables match those in the question Box 2: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2A3, 5+4) Enter DNE for Does Not Exist, 00 for Innity Box 3: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2A3, 5+4) Enter DNE for Does Not Exist, 00 for Innity Alicia's car was worth $12,000 at the beginning of 2000 and the value of the car decreased exponentially, decreasing by 22% each year. a. Write a function f that determines the value of Alicia's car (in dollars) in terms of the number of years t since the beginning of 2000. for) = E Preview b. How many years after the beginning of 2000 was Alicia's car worth $6,000? |:I Previev c. How many years after the beginning of 2000 was Alicia's car worth $2,000? |:] Preview Box 1: Enter your answer as an expression, Example: 3x"2+1, x/S, (a+b)/c Be sure your variables match those in the question Box 2: Enter your answer as a number (like 5, 3, 2.2172) or as a calculation (like 5/3, 2A3, 5+4) Enter DNE for Does Not Exist, 00 for Innity Box 3: Enter your answer as a number (like 5, -3, 22172) or as a calculation (like 5/3, 28, 5+4) Enter DNE for Does Not Exist, 00 for Innity A standard piece of paper is 0.05 mm thick. Let's imagine taking a piece of paper and folding the paper in half multiple times. We'll assume we can make "perfect folds," where each fold makes the folded paper exactly twice as thick as before - and we can make as many folds as we want. a. Write a function 9 that determines the thickness of the folded paper (in mm) in terms of the number folds made, 11. (Notice that 9(0) : 0.05.) we) = : Prewiew b. The function g has an inverse. The function g _ 1 determines the number of folds needed to give the folded paper a thickness of t mm. Write a function formula for g _ 1. Me) = :1 Preview 0. Use your function in part (b) to determine how many times you must fold a piece of paper to make the folded paper have a thickness that is the same as the distance from the earth to the moon. (Assume the distance from the earth to the moon is 384,472,300,000 mm). S reirir Preview Box 1: Enter your answer as an expression. Example: 3x"2+1, x/5, (a+b)/c Be sure your variables match those in the question Box 2: Enter your answer as an expression. Example: 3x"2+1, x/5, (a+b)/c Be sure your variables match those in the question Box 3: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 513, 2A3, 5+4) Enter DNE for Does Not Exist, 00 for Innity At the beginning of 2000 Todd's house was worth 226 thousand dollars and Dylan's house was worth 128 thousand dollars. At the beginning of 2003, Todd's house was worth 174 thousand dollars and Dylan's house was worth 158 thousand dollars. Assume that the values of both houses vary at an exponential rate. a. Write a mction f that determines the value of Todd's house (in thousands of dollars) in terms of the number of years t since the beginning of 2000. flt) = :1 Preview b. Write a function 9 that determines the value of Dylan's house (in thousands of dollars) in terms of the number of years t since the beginning of 2000. g(t) : Preview 0. How many years after the beginning of 2000 will Todd's and Dylan's house have the same value? Note: Be careful that your parentheses are correct so that your answer is interpreted as you intend. :l years Preview Box 1: Enter your answer as an expression. Example: 3x"2+l, x/5, (a+b)/c Be sure your variables match those in the question Box 2: Enter your answer as an expression. Example: 3x\"2+1, x15, (a+b)/c Be sure your variables match those in the question Box 3: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2A3, 5+4) Enter DNE for Does Not Exist, 00 for Innity Suppose f(:c) = 7(2.9)I and g(m) 2 59(15):\". Solve f(x) = g(:c) for m. a: : Preview Box 1: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2A3, 5+4) Enter DNE for Does Not Exist, 00 for Innity Submit A point moves along a straight path. The function f (t) = log3(t) determines the distance (in meters) the point has traveled in terms of the number of seconds t since the point started moving. a. How far has the point traveled 23 seconds after it started moving? |:| meters Preview b. If the point has traveled 1.89279 meters, how many seconds have elapsed since it started moving? |:| seconds Preview 0. Write a function f _ 1 that determines the number of seconds that have elapsed since the particle started moving in terms of the distance (in meters) the particle has traveled, d. rm = :1 Preview Box 1: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2A3, 5+4) Enter DNE for Does Not Exist, 00 for Innity Box 2: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2A3, 5+4) Enter DNE for Does Not Exist, 00 for Innity Box 3: Enter your answer as an expression. Example: 3x"2+1, x/5, (a+b)/c Be sure your variables match those in the question Stephen's body metabolizes caffeine at a rate of 13.1% per hour (so the amount of caffeine in Stephen's body decreases by 13.1% each hour). a. If Stephen consumes a cup of coffee with 90 mg of caffeine in it, how long will it take for Stephen's body to metabolize half of the 90 mg of caffeine? :1 hours Preview b. If Stephen consumes an energy drink with 198 mg of caffeine in it, how long will it take for Stephen's body to metabolize half of the 198 mg of caffeine? hours Preview 0. If Stephen consumes a cup of coffee with c mg of caffeine in it, how long will it take for Stephen's body to metabolize half of the c mg of caffeine? (Hint: your answer will be a numerical value.) : heure Preview Box 1: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2A3, 5+4) Enter DNE for Does Not Exist, 00 for Innity Box 2: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2A3, 5+4) Enter DNE for Does Not Exist, 00 for Innity Box 3: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2A3, 5+4) Enter DNE for Does Not Exist, 00 for Innity