Certainly! Let's break down the solution for these two expressions step-by-step.
### First Equation Calculation:
[tex]\[ 1000(1 + 0.5)^5 \][/tex]
1. Identify the base, rate, and time:
- Base = 1000
- Rate = 0.5
- Time = 5
2. Add the rate to 1:
[tex]\[ 1 + 0.5 = 1.5 \][/tex]
3. Raise 1.5 to the power of the time (5):
[tex]\[ 1.5^5 \][/tex]
4. Multiply the base by the result of the power calculation:
[tex]\[ 1000 \times (1.5^5) \][/tex]
5. Get the final answer for the first equation:
[tex]\[ 1000 \times 7.59375 = 7593.75 \][/tex]
### Second Equation Calculation:
[tex]\[ 80000(1.17)^2 \][/tex]
1. Identify the base, rate, and time:
- Base = 80000
- Rate = 0.17
- Time = 2
2. Add the rate to 1:
[tex]\[ 1 + 0.17 = 1.17 \][/tex]
3. Raise 1.17 to the power of the time (2):
[tex]\[ 1.17^2 \][/tex]
4. Multiply the base by the result of the power calculation:
[tex]\[ 80000 \times (1.17^2) \][/tex]
5. Get the final answer for the second equation:
[tex]\[ 80000 \times 1.34289 = 109511.99999999999 \][/tex]
### Summary of Results:
- The result of [tex]\( 1000(1 + 0.5)^5 \)[/tex] is [tex]\( 7593.75 \)[/tex].
- The result of [tex]\( 80000(1.17)^2 \)[/tex] is [tex]\( 109511.99999999999 \)[/tex].
Thus, the detailed step-by-step evaluation leads us to the final answers:
[tex]\[ \boxed{7593.75 \text{ and } 109511.99999999999} \][/tex]
