His money in the savings account is given by m(t)= [tex] 50t^2+100t+80 [/tex]
The rate at which he is saving money can be obtained by differentiating the function.
m'(t)= 100t+100
So, in one year he saves
100[tex] \times [/tex]1+100=200
In two years he saves
100[tex] \times [/tex]2+100=300
In three years he saves
100[tex] \times [/tex]3+100=400
Therefore, time taken to save 1000 dollars is
100t+100=1000
100t=900
[tex] t=\frac{900}{100} [/tex]
t=9
Therefore, it will take 9 years to save $1000.
