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 , for (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

Answer and Step-by-step explanation:

(1) Scale factor is a constant value that multiplies another value. For a puppy's weight, scale factor is 1.23.

The percentage growth is

1.23 = 1 + 0.23

Percentage is 0.23 or 23%.

(2) Equation for increase is

$w=365(1.23)^{t}$

When w = 4000g:

$4000=365(1.23)^{t}$

$(1.23)^{t}=\frac{4000}{365}$

$1.23^{t}=10.96$

Using the log law:

$log_{b} (M^{k}) = klog_{b}(M)$

$log(1.23^{t})=log(10.96)$

t.log(1.23) = log(10.96)

0.08990t = log(10.96)

$t=\frac{log10.96}{0.08990}$

t = 11.56

The puppy will weigh 4000 grams in 11 and half weeks or between 11 and 12 weeks.