Answer:
38.1 months
Step-by-step explanation:
For a pole-vaulter in training, the height the athlete will be able to pole-vault after t months of training is given by the function:
[tex]H(t)=20-15e^{-0.02t}[/tex]
To find out after how many months the pole-vaulter will be able to vault 13 feet, set substitute H(t) = 13 and solve for t:
[tex]13=20-15e^{-0.02t}\\\\\\15e^{-0.02t}=20-13\\\\\\15e^{-0.02t}=7\\\\\\e^{-0.02t}=\dfrac{7}{15}\\\\\\\ln\left(e^{-0.02t}\right)=\ln\left(\dfrac{7}{15}\right)\\\\\\-0.02t\ln(e)=\ln\left(\dfrac{7}{15}\right)\\\\\\-0.02t(1)=\ln\left(\dfrac{7}{15}\right)\\\\\\-0.02t=\ln\left(\dfrac{7}{15}\right)\\\\\\t=\dfrac{\ln\left(\dfrac{7}{15}\right)}{-0.02}\\\\\\t=38.1070026023...[/tex]
Therefore, the pole-vaulter will be able to vault 13 feet after approximately 38.1 months (rounded to the nearest tenth).
