Question

50 Point Question...

A dog owner observes that from birth to age 14 weeks, the puppy’s weight can be modelled by the equation w = 365×(1.23)t (0 ≤ t ≤ 14),

(1) Write down the scale factor, and use this to find the percentage increase in the weight each week.

(2) Use the law of logs to find the age at which the puppy will weigh 4000 grams

Answer 1

See explanation

Explanation:

A dog owner observes that from birth to age 14 weeks, the puppy’s weight can be modelled by the equation

`w = 365\cdot (1.23)^t \ (0\le t \le  14)`

In this equation,

• number 365 represents the initial weight of puppy;
• number 1.23 can be rewritten as 1+0.23, where 0.23 (or 23%) is the rate of weight increase.

When w=4,000, then

`4,000=365\cdot (1.23)^t\\ \\(1.23)^t =(4,000)/(365)=(800)/(73)\\ \\t=\log_(1.23)(800)/(73)\approx 11.5651`

This means that puppy will weight 4,000 grams nearly at the middle between 11th week and 12th week.