## Thinking Mathematically (6th Edition)

Fill the blank with $31+2.4x$
The initial percentage was 31 (percent). After one year, it increases by 2.4, meaning that 2.4 is added to 31, which we write as 31+2.4. After two years, the one-year total is again increased so it equals (31+2.4)+2.4 = 31+2(2.4) After three years, the two-year total is again increased so it equals 31+2(2.4)+2.4 = 31+3(2.4) ... Recognize the pattern. Starting with the value 31, after x years, it had increased x times, each time by 2.4. The total increase is $x\cdot 2.4$ Adding to the starting value, (starting value)+(total increase), equals $31+x\cdot 2.4$ or $31+2.4x$ Fill the blank with $31+2.4x$