Answer:
9.3 years
Step-by-step explanation:
we know that
The equation of a exponential growth is equal to
[tex]y=a(1+r)^x[/tex]
where
y is the weight in pounds
x is the number of years
a is the initial value or y-intercept
we have
[tex]a=70\ lb\\r=50.5\%=50.5\100=0.505[/tex]
substitute
[tex]y=70(1+0.505)^x[/tex]
[tex]y=70(1.505)^x[/tex]
For y=3,100 lb
substitute in the equation
[tex]3,100=70(1.505)^x[/tex]
solve for x
[tex]\frac{310}{7} =(1.505)^x[/tex]
apply log both sides
[tex]log(\frac{310}{7}) =log[(1.505)^x][/tex]
[tex]log(\frac{310}{7}) =(x)log(1.505)[/tex]
[tex]x=log(\frac{310}{7})/log(1.505)=9.3\ years[/tex]
