Task 3 A Log's Purpose As we continueto think about modelingwith mathematics there are some situationswhere we do more than just model a set of data or a graph with a function Sometimeswe use an existing model in a contextto create a different model that relates the variablesin a different way. This gives us different things to solve for and a uniqueway to representthe situation with graphs The list gives some scenarioswe can use exponentialfunctionsto model. Study each scenario and the function that models it, then answer the questionsthat follow. . David estimatedhe had about 20 fish in his pond. A year later, there were about 1.5 times as many fish. The year after that, the number of fish increased by a factor of 1.5 again. The number of fish is modeled by f(x) = 20(1.5)*. . The price of gas, which started at $2.56 per gallon, increasedat a rate of 4% per year. The price of gas is modeled by f(x) = 2.56(1.04)* . The chess club started with a membershipof only 4 students but the membershipgrew at a rate of 2.56% each week. The number of students is modeled by f(x) = 4(1.0256)*. . A forest started with 256 maple trees, and the number of maple trees increased at a rate of 40% each year. The number of trees is modeled by f(x) = 256(1.4)*. . In 2001, a plot of land was worth $12,000. Each year, the value of the plot increasesby 8%. The value of the plot is modeled by f(x) = 12,000(1.08)* . Liam buys a motorcyclefor $2,900. Its value depreciatesannuallyat a rate of 12%. Its value is modeled as p(x) = 2,900(0.88)*. . A nonnativefern species is introducedinto an area and quickly begins to die. The number of plants is modeled by p(n) = 1,200(0.8)". . A radioactivesubstancewith a mass of 64 grams decays at a rate of 25% every hour. The mass of the substanceis modeled by m(x) = 64(0.75). PartA Choose one of the scenariosfrom the list, and create a question you could ask that could be answeredonly by graphing or using a logarithm