Final answer:
The time taken for the third unit given a learning rate of 0.81 and an initial time of 12 for the first unit is calculated using the formula T(n) = T(1) × r^(n-1). The result is approximately 7.87 when rounded to two decimal places.
Step-by-step explanation:
The question asks about calculating the time taken to complete the third unit of work given a learning rate and the time taken for the first unit. The learning rate is a concept used in mathematics and economics to describe the rate at which performance or productivity improves through practice or production.
Here, a learning rate of 0.81 indicates that each subsequent unit of work takes 81% of the time that the previous unit took. To find the time for the third unit, the formula we use is T(n) = T(1) × r^(n-1), where T(n) is the time for the nth unit, T(1) is the time for the first unit, r is the learning rate, and n is the unit number.
To calculate the time it takes to complete the third unit:
- Plug the values into the formula: T(3) = 12 × 0.81^(3-1).
- Calculate the exponent part: 0.81^2 = 0.6561.
- Multiply the base time for the first unit by the result of the exponent calculation: 12 × 0.6561 = 7.8732.
To two decimal places, the time taken for the third unit is 7.87.
The complete question is: You have a learning rate of 0.81 . If the first unit takes 12 , how long does the third unit take? Answer to 2 decimal places. Only enter the number without the units. is: