Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year. how many years will it take for carbon–14 to decay to 10 percent of its original amount? the equation for exponential decay is at = a0e–rt.

18569.234 years

Step-by-step explanation:

Given : Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year.

To Find: How many years will it take for carbon–14 to decay to 10 percent of its original amount?

Solution:

The equation for exponential decay is

= initial amount

A(t) = Amount after t time

Now we are supposed to find after how many years will it take for carbon–14 to decay to 10 percent of its original amount.

So,

r = 0.0124 % = 0.000124

Substitute the values in the equation:

Hence it will take 18569.234 years to decay to 10 percent of its original amount.

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2

answer by yourhope:

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