Show all work for full marks. Use the following information to answer the next question. For Leila, caffeine has a half-life of approximately 6 h. If Leila ingests 250 mg of caffeine, the amount of caffeine in her body over time can be modelled by the exponential function R = 250 1 6 where R is the amount of caffeine in Leila's body, in milligrams, after t hours. 1. Leila no longer experiences the effects of caffeine once the amount of caffeine in her body drops to 50 mg. Explain how to graphically determine the amount of time that it would take Leila to no longer experience the effects of the caffeine ingested. [2] 2. Algebraically solve the following. [6] a) 43x = 83x-6 b) 4.2(*-1) = 64 (*+1) c) 36(-3x+3) 1 2163. Complete the table. [1] Use thefoowing information to answer the next two questions. The table below show the population in a community since 2012. - _ These data can be modelled by an exponential regression function of the form P = a - br where P is the population in the community after t years since 2012. 4. Write the equation of the exponential function that models the population in the community since 2012. Round your value of a to the nearest whole number and the value of b to the nearest hundredth. [1] Use the following information to answer the next part of the question. If the population in the community was actually half of what was originally stated in 2012, then the equation that models the population in the community since 2012 can be written as a new exponential function. 5. Compare the equation of the new mction to the equation of the original mction in terms of the information about the population in the community since 2012. [2]