# What is the y-intercept for this function and what does it represent?

Growth and Decay Functions a) If you invest $1250 in an account that earns 6% compounded quarterly, the amount you will have in the account, S(x), after x years is given byS left parenthesis x right parenthesis equals space 1250 left parenthesis 1.015 right parenthesis to the power of 4 x end exponentCalculate the amount of money in the account, S(x), after 2, 4, 6, 8, and 10 years and the interest earned in the account.xS(x)Interest2

4

6

8

10

Is this an exponential growth or decay function? How much more money would you earn in interest if you left the money in the account 10 years instead of 4 years? What is the S – intercept (y-intercept) for this function and what does it represent?

b) In 1986, the worst nuclear disaster occurred in Chernobyl, USSR, when an explosion at a nuclear power plant released 1000 kg of radioactive cesium-137. The following model calculates the remaining amount of cesium-137 in the atmosphere x years after 1986.f left parenthesis x right parenthesis equals 1000 left parenthesis 0.5 right parenthesis to the power of x divided by 30 end exponent

Find for the following:Yearx (years since 1986)f(x)200620

202640

204660

206680

2086100

2106120

2126140

If 100 kg or more of cesium-137 is considered unsafe for humans, when will this area be safe again (you may give an estimate based on your table of values above or find the exact value from a graphing utility)? What is the y-intercept for this function and what does it represent? Is this a growth or decay function?