[Video] Q10: F(n) = 5.77(0.98^n)the function above can be used to estimate the number of farms, f(n), in millions, in the united states for 0 < n < 72, where n is the number of years after 1940. which of the following is the best interpretation of the number 5.77 in this context?

Explanation for Question 10 From the Math (No Calc) Section on the 2018 May Sat

Question 10 says the function above can be used to estimate the number of 2 farms AF event in millions in the United States for N 3 is greater than or equal to zero and less than or equal to 72. 4 Where N is the number of years after 1940, 5 which of the following is the best interpretation of the number of 5.77 in 6 this context. So to help us figure out the answer to this problem, 7 I've written down the formula for exponential functions down at the bottom here. 8 So the value outside of the parentheses, 9 that's represented by the variable a and that represents the initial value of 10 whatever is changing in quantity. Then R represents the rate 11 of increase or decrease depending on whether it's a decay or growth function and 12 T represents the amount of time. So if we want to know what 5.77 13 equals, we just look to where it is in the equation it's outside of 14 the parentheses, which means that it's the initial value of whatever is changing. 15 So since the thing that's changing in quantity is the amount of farms. 16 5.77 represents the amount of farms at the start. 17 And since that started being measured in 1940, 18 that we know that the answer is a, the estimated number of farms in 19 millions in 19.