Cobalt-57 is used in medical testing and has a half-life of about 272 days, which means after 272 days, half of the Cobalt-57 has decayed to a less radioactive and more stable form. The function for the half-life of an isotope is shown below. General half life formula

A0 is the initial amount of the isotope, h is the half-life, t is the input or time elapsed, and A(t) is the output or the amount of the isotope remaining as a function of time.

1. What type of function does this seem to represent? Explain your reasoning using complete sentences. (6 points)

2. Let's say you have 500 grams of cobalt-57. Substitute the half-life and initial amount values into the function. Enter the new function. (6 points)

3. If the initial amount of cobalt-57 were to double, what type of transformation would that be from the function in question 2? Explain your reasoning and enter the new function. (6 points)

4. If the half-life, h, were to double, what type of transformation would that be from the function in question 2? Explain your reasoning and enter the new function. (6 points)

5. Rewrite the half-life function from question 2 using the rules of exponents to make the exponent negative and the base of the function greater than 1. Enter your new function. (6 points)

Refer back to the first practical assessment in this unit regarding cobalt-57 and half life.

1. Find the inverse of the function from question 2 in that practical assessment. Make sure you enter each step or insert an image of your written work. You can't use natural log (LN).(15 points)

2 . What does the input variable of the inverse function represent? (5 points)

3. What does the output variable of the inverse function represent? (5 points)

4. If 100 grams of cobalt-57 has decayed to 62 grams, how much time has passed? (5 points)