Jerry invests $6000 at 7.5% a, compounded annually.
a) Determine the equation of the amount, A
, after t
years.
b) Estimate the instantaneous rate of change in the value at 10 years.
c) Suppose that the interest rate was compounded semi-annually instead of annually. What would the instantaneous rate of change be at 10 years?
For 500 g of a radioactive substance with a half-life of 5.2 h, the amount remaining is given by the formula \displaystyle{M(t)=500(0.5)^{\frac{t}{5.2}}}
where M
is the mass remaining and t is the time in hours.
a) Calculate the amount remaining after 1 day.
b) Estimate the instantaneous rate of change in mass at 1 day.