In the exponential growth function y = 235(1.15)^x, what is the 1. growth factor? _____________ 2. percent increase? _____________
Accepted Solution
A:
Growth Factor: 1.15 The y-values multiply by 1.15 every unit you increase x by. Percentage Increase: 15% If we are multiplying y-values by 1.15 for every unit of x, we are finding 115% (= 1.15 × 100) of the previous value of y; 100% is equivalent to the previous value, so effectively, we are just adding to the previous value 15% of itself to get the next value. E.g. If x = 1, then: y = 235(1.15)¹ = 270.25; The y-value when x = 2 is just: 270.25 + (15% of 270.25) = 270.25 + (270.25 × (15/100)) = 270.25 + (40.5375) = 310.7875 The easier way to write and represent this for any value of x is: y = 235(1.15)ˣ