Question

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The function t relates the age of a plant fossil in years to the percentage c of carbon remaining in the fossil relative to when it was alive.
t(c)=-3970.9(ln c)

Use function t to complete the statements.

A fossil with 47% of its carbon remaining is approximately how old
1. 2998
2 11,910
3 7550

A fossil that is 7000 years old will have approximately
1. .2%
2. 57%
3 17%

Of its carbon remaining.

Select the correct answers

Answer 1

Answer: For plato family

The function t relates the age of a plant fossil, in years, to the percentage, c, of carbon-14 remaining in the fossil relative to when it was alive.

Use function t to complete the statements.

A fossil with 47% of its carbon-14 remaining is approximately

years old.

A fossil that is 7,000 years old will have approximately

17% of its carbon-14 remaining.

Explanation:

The first box is 2,998

The second box is 17%

Answer 2

2998 ; 17%

Explanation:

Given the function:

t(c)=-3970.9(ln c)

c = % of carbon remaining ; t = time

1.) c = 47% = 47/100 = 0.47

t(0.47) = - 3970.9(In 0.47)

t = - 3970.9 * −0.755022

t = 2998.119

t = 2998

B.)

t = 7000

t(c)=-3970.9(ln c)

7000 = - 3970.9(In c)

7000 / - 3970.9 = In c

−1.762824 = In c

c = exp(−1.762824)

c = 0.1715596

c = 0.1715596 * 100%

c = 17.156% ; c = 17%