Final answer:
After doubling $178 five times, the final value will be $5,696. This is sixteen times the original amount because the money is doubled, which means multiplied by 2, five times in succession.
Step-by-step explanation:
To determine the value after doubling $178 five times, we use the concept of exponential growth, which is similar to compound interest. Each time the amount is doubled, it means it's multiplied by 2. Therefore, if we double $178 once, we get $178 × 2 = $356. If we double $356, we get $356 × 2 = $712, and we continue this process five times.
Here is the calculation for each step:
- First doubling: $178 × 2 = $356
- Second doubling: $356 × 2 = $712
- Third doubling: $712 × 2 = $1,424
- Fourth doubling: $1,424 × 2 = $2,848
- Fifth doubling: $2,848 × 2 = $5,696
The value after doubling $178 five times is $5,696. This is sixteen times the original value since 25 (2 × 2 × 2 × 2 × 2) equals 32, and $178 × 32 = $5,696.