Radioactive decay. Carbon-14 has a decay rate of 0.012097% per year. The rate of change of an amount N of carbon-14 is given by where t is the number of years since decay began.

a) Let N0 represent the amount of carbon-14 present at t = 0. Find the exponential function that models the situation.

b) Suppose 200 g of carbon-14 is present at t = 0. How much will remain after 800 yr?

c) After how many years will half of the 200 g of carbon-14 remain?

You drop a rubber ball off the roof of a 50 meter high building onto a paved parking lot. it bounces back up with every bounce, but not quite all the way back up to you. after the first bounce it bounces back only 80 percent of the distance it was dropped from. the pattern continues, meaning after every bounce it comes up to just 80 percent of the previous maximum height. so if before the first bounce the height is 50 meters, what height does the ball reach after the fifth bounce? round your answer to one decimal place and chose the correct response from the choices below:

The graph represents the gallons of water in a water tank with respect to the number of hours since it was completely filled

If you apply the changes below to the linear parent function f(x)=x what is the equation of the new function vertically stretched by a factor of 3 flip over the x axis