Answer
Fill the blank with
$31+2.4x$
Work Step by Step
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
$31+2.4x$
