A population of butterflies grows in such a way that each generation is simply 1.5 times the previous generation. There were 350 butterflies in the first generation, how many will there be by the 19th generation?Answer the question with all work shown. Thanks

Accepted Solution

Answer:378.5 or just 378Step-by-step explanation:This is a linear model with x representing the number of generations that's gone by, y is the number of butterflies after x number of generations has gone by, and the 350 represents the number of butterflies initially (before any time has gone by.  When x = 0, y = 350 so that's the y-intercept of our equation.)The form for a linear equation is y = mx + b, where m is the rate of change and b is the y-intercept, the initial amount when x = 0.Our rate of change is 1.5 and the initial amount of butterflies is 350, so filling in the equation we get a model of y = 1.5x + 350.If we want y when x = 19, plug 19 in for x and solve for y:y = 1.5(19) + 350y = 378.5Since we can't have .5 of a butterfly we will round down to 378