Respuesta :
Answer:
7.2 years
Step-by-step explanation:
[tex]f(t) =200(1 - 0.956e^{-0.18t})[/tex]
where f(t) is the length and t is the number of years old
given the Mike measures 148 cm, we need to find out the age
So we plug in 148 for f(t) and solve for t
[tex]148 =200(1 - 0.956e^{-0.18t})[/tex]
divide both sides by 200
[tex]\frac{148}{200} = 1 - 0.956e^{-0.18t}[/tex]
Now subtract 1 from both sides
[tex]-0.26= - 0.956e^{-0.18t}[/tex]
Divide both sides by -0.956
[tex]\frac{0.26}{0.956} =e^{-0.18t}[/tex]
Now take ln on both sides
[tex]\frac{0.26}{0.956} =e^{-0.18t}[/tex]
[tex]ln(\frac{0.26}{0.956} )=-0.18tln(e)[/tex]
[tex]ln(\frac{0.26}{0.956} )=-0.18t[/tex]
divide both sides by -0.18
t=7.2
So 7.2 years
