I need the answers to this 3 part question plz

Question

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 less radioactive and more stable form. The function for the half-life of an isotope is shown.

A(t)=A₀(1/2)^t/h

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

1)Lets say you have 500 grams of cobalt -57. Substitute the half-life and initial amount values into the function. Enter the new function.

a)If the initial amount of cobalt -57 were to double, what type of transformation would be from the function of the first question? Explain then enter the new function.

b)If the half-life,h, were to double what type of transformation would that be from the function of the first question? Explain then enter the new function.

c)Rewrite the half-life function from the first question using the rules of exponents to make the exponent negative and the base function greater. Enter the new function.

Answer 1

1. A(t) = 500 * (1/2)^t/500
2. The transformation would be a steeper decay downwards because if you're starting out with a higher amount of a decaying substance, the decay rate would be faster since more units of the substance are decaying given a certain amount of time. A(t) = 1000 * (1/2)^t/500
3. The transformation would be a less steeper decay downwards because if the half-life is higher, then the decay rate would be slower since less units of the substance are decaying given a certain amount of time. A(t) = 500 * (1/2)^t/1000
4. The negative exponent of a number is the reciprocal of it. A(t) = 500 * 2^-t/500