Question

A hippopotamus's typical growth rate is typically 50.5% per year when considering it's weight in pounds from birth to maturity. Using the continuous growth equation, how long would it take a 70lb infant hippo to reach an average adult weight of 3100lbs?

Answer 1

Answer:

9.3 years

Step-by-step explanation:

we know that

The equation of a exponential growth is equal to

$y=a(1+r)^x$

where

y is the weight in pounds

x is the number of years

a is the initial value or y-intercept

we have

$a=70\ lb\\r=50.5\%=50.5\100=0.505$

substitute

$y=70(1+0.505)^x$

$y=70(1.505)^x$

For y=3,100 lb

substitute in the equation

$3,100=70(1.505)^x$

solve for x

$\frac{310}{7} =(1.505)^x$

apply log both sides

$log(\frac{310}{7}) =log[(1.505)^x]$

$log(\frac{310}{7}) =(x)log(1.505)$

$x=log(\frac{310}{7})/log(1.505)=9.3\ years$