Situation: A geologist in South America discovers a
bird skeleton that contains 47% of its
original amount of C-14.
N = Noekt
No = inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
k= 0.0001
t = time, in years

Find the age of the bird skeleton to the nearest year.

7550 years

Step-by-step explanation:

From;

N = Noe^-kt

No = inital amount of C-14 (at time  t = 0)

N = amount of C-14 at time t

k= 0.0001

t = time, in years

Now we have been told in the question that N =0.47 No

So we have;

0.47 No = Noe^-0.0001 t

0.47 No/No = e^-0.0001 t

0.47 = e^-0.0001 t

ln 0.47 = ln e^-0.0001 t

-0.7550 = -0.0001 t

t = 0.7550/0.0001

t = 7550 years

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places

it is 10.6 according to my calculations