1. a. What function V(x) gives the value of the coin that the general received on day x? (2 pts)
V(x)=2ˣ⁻¹ denarii
b. What is the domain of this function? (1 pt)
Integer x>0
2. Write a function M(x) that gives the mass of each coin in kilograms as a function of day x. (2
pts)
M(x)=0.006(2ˣ⁻¹) kg
3. a. Use M(x) from Question 2 to write an inequality that describes the mass of a coin that the
general could carry or roll out of the treasury. (2 pts)
M(x)≤300, 0.006(2ˣ⁻¹)≤300, 2ˣ⁻¹≤300/0.006=300000/6=50000, 2ˣ⁻¹≤50000, x-1≤log₂50000. Since 2¹⁶=65536, x-1<15, M(16)≤0.006×32768=196.608kg.
b. Make a table of values of this function. (3 pts)
x 2ˣ⁻¹ M (kg)
1 1 0.006
2 2 0.012
3 4 0.024
4 8 0.048
5 16 0.096
6 32 0.192
7 64 0.384
8 128 0.768
9 256 1.536
10 512 3.072
11 1024 6.144
12 2048 12.288
13 4096 24.576
14 8192 49.152
15 16384 98.304
16 32768 196.608
17 65536 393.216
c. Use the table to solve the inequality. (2 pts)
M≤196.608
4. What is the total value of the coins that the general would receive?
32768 denarii
