Question

Christina has some money at home, and the amount is modeled by the function h(x) = 103. She read about a bank that has savings accounts that accrue interest according to the function s(x) = (1.03)x − 1. Using complete sentences, explain to Christina how she can combine her functions to create a new function, and explain what this new function means.

Answer 1

x usually represents time in months, and when you say h(x) = 103, this is a constant function, flat all throughout as x→∞. For s(x), it represents a line with increasing value of s(x) as x→∞ at a rate of 1.03 and intercept of -1 at s(x) axis. When you say "combine" to form a new function means the addition of the two given functions, that is, h(x) + s(x), say equal to g(x).

g(x)=h(x)+s(x)=103+1.03x−1=1.03x+102g(x)=1.03x+102

The new function g(x) is the same as s(x) with respect to the rate of increase, equal to 1.03, except this time, the intercept is +102, g(x) is the shifted version of s(x), from -1 to +102 (due to h(x)=103). Her savings account in a bank will grow at a rate of 3% per unit of time (x), starting at a savings of 102 at x=0.