To find out how much weight the machine can lift on the fifth day, we start with the initial weight it can lift on the first day, which is 10 kg. The weight increases by 20 percent each day.
The formula to calculate the weight lifted on any given day is:
\[ \text{Weight on day } n = \text{Initial weight} \times (1 + \text{percentage increase})^{(n-1)} \]
In this case, the initial weight is 10 kg and the percentage increase is 20% (which is expressed as 0.20 in decimal form). Therefore, the formula becomes:
\[ \text{Weight on day } n = 10 \times (1 + 0.20)^{(n-1)} \] \[ \text{Weight on day } n = 10 \times (1.20)^{(n-1)} \]
Now, we need to find the weight on the fifth day (n = 5):
\[ \text{Weight on day 5} = 10 \times (1.20)^{4} \]
Now we calculate \( (1.20)^{4} \):
\[ (1.20)^{4} = 1.20 \times 1.20 \times 1.20 \times 1.20 \] \[ = 1.20 \times 1.20 = 1.44 \] \[ = 1.44 \times 1.20 = 1.728 \] \[ = 1.728 \times 1.20 = 2.0736 \]
Now we substitute this back into our formula:
\[ \text{Weight on day 5} = 10 \times 2.0736 = 20.736 \]
Rounding to two decimal places, the weight that the machine can lift on the fifth day is:
\[ \boxed{20.74} \text{ kg} \]