Final Answer:
The puppy weighs approximately 1.76 pounds when he is six weeks old.
Step-by-step explanation:
In this scenario, the puppy's weight follows a geometric progression. The initial weight (a₀) is given as 0.85 lb, and each week the weight increases by 24%. The formula to calculate the nth term (aₙ) in a geometric progression is aₙ = a₀ * (1 + r)^(n-1), where r is the common ratio. In this case, the common ratio (r) is 24%, or 0.24 when expressed as a decimal.
To find the puppy's weight at six weeks (a₆), substitute the values into the formula:
\[a₆ = 0.85 * (1 + 0.24)^5\]
\[a₆ ≈ 0.85 * (1.24)^5\]
\[a₆ ≈ 0.85 * 2.867\]
\[a₆ ≈ 1.76\]
Therefore, the puppy weighs approximately 1.76 pounds at the end of the sixth week.
In this calculation, each week's weight gain is compounded, leading to an exponential increase. The expression (1 + r)^(n-1) represents the growth factor for each week. The iterative calculation is crucial for accurately determining the puppy's weight at the specified time. The result, 1.76 pounds, reflects the cumulative effect of the weekly weight gains, providing a comprehensive understanding of the puppy's growth over the six-week period.