Need help asap for college algebra practice

Question

1) The amount of​ carbon-14 present in a paint after t years is given by y=yoe^-0.00012t. The paint contains 18​% of its​ carbon-14. How old are the​ paintings?

2) Suppose an Egyptian mummy is discovered in which the amount of​ carbon-14 present is only about

three​-fourths the amount found in living human beings. The amount of​ carbon-14 present in animal bones after t years is given by

y=y 0 e ^ -0.0001216t where y 0 is the amount of​ carbon-14 present in living human beings. About how long ago did the Egyptian​ die?

Answer 1

1.) For y=y₀*e^-0.00012t

y=the amount of carbon left in a painting

y₀=the initial amount of carbon

t=the amount of time passed (in years)

So this problem can be outlines with

y = y₀*0.18 (Because the amount of carbon left is 18% of the initial carbon)

y₀ = y₀

t = t (what we are trying to find)

Our new equation is

y₀*0.18 = y₀*e^-0.00012t *y₀ cancels

0.18 = e^-0.00012t

ln(0.18)=ln(e^-0.00012t) *using properties of logs, ln(e^y)=y

ln(0.18)=-0.00012t

t=14289.99 years

They are 14289.99 years old.

2.) Similar to above, y=y₀*e^-0.0001216t

y = y₀*0.75 (Because the amount of carbon left is 3/4ths of the initial carbon)

y₀ = y₀

t = t (what we are trying to find)

y₀*0.75=y₀*e^-0.0001216t

0.75=e^-0.0001216t

ln(0.75)=ln(e^-0.0001216t)

ln(0.75)=-0.0001216t

t=2365.8056 years

They died 2365.8056 years ago.