Answer:
The equation 100·(1.02)2t, models the growth of the bond's value over time when the bond grows at a rate of 2% every half-year. Here's the breakdown:
The "100" represents the initial value of the bond when it is first purchased.
The "(1.02)" represents the growth factor for each half-year period. A 2% growth rate means that each half-year, the bond's value is multiplied by 1.02 (since 2% as a decimal is 0.02, and adding this to 1 gives us the growth factor for one period).
The exponent "2t" represents the number of half-year periods that pass in "t" years. Since there are 2 half-years in a year, the bond's value compounds 2 times per year.
So, each time "t" increases by 1 (which is one year), the exponent effectively increases by 2 because the bond grows twice a year (once every half-year). Thus, the value of the bond after "t" years is correctly given by 100·(1.02)2t, with the growth being compounded semiannually.
