Rate of Change (Another One)?

A puppy weighs 2.0 lbs at birth and 3.5 lbs two months later. If the weight of the puppy during its first 6 months is increasing at a rate of proportional to its weight, then how much will the puppy weigh when it is 3 months old?

Steps please!

Rate of Change (Another One)?

The statement in math terms%26quot;

dw/dt = k w, t in months.

dw/w = k dt

ln w = kt

w = exp(kt)+ const

we have two unknowns, k and the constant.

we have two known points on the function curve,

at t=0: 2 = 1 +const, =%26gt; const=1

at t=2: 3.5 = exp(2k)+1

2.5= exp(2k)

0.9 = 2k (approx)

k=0.45 appx

at t=3: w = exp(1.35) + 1

w = 5 lbs appx

Rate of Change (Another One)?

i think you need to rephrase the question...you said that the puppy%26#039;s weight increases proportionally to its weight. did you mean age?

Rate of Change (Another One)?

About 37% growth rate about 5.2 pounds.