Question

The amount of money in brian's savings account is given by the function m (t) = 50t 2 + 100t + 80, where t is the time in years. approximately how many years will it take brian to save $1,000?

Answer 1

His money in the savings account is given by m(t)= $50t^2+100t+80$

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$\times$1+100=200

In two years he saves

100$\times$2+100=300

In three years he saves

100$\times$3+100=400

Therefore, time taken to save 1000 dollars is

100t+100=1000

100t=900

$t=\frac{900}{100}$

t=9

Therefore, it will take 9 years to save $1000.