If an initial quantity continuous decay at an exponential rate , then the final amount after a time is given by the following formula .

Half life of carbon - is thousand years.

Since half life of carbon - is .

Substitute and in .

Apply logarithm on each side.

.

(a)

Find modeling equation for exponential decay.

Substitute in .

.

Modeling equation for exponential decay is .

(b)

Find how many grams of carbon- will remain after thousand years.

Initial carbon- is grams.

Substitute , and in .

grams.

carbon- will remain after thousand years is grams.

(c)

Find when only gram of the original grams of carbon- will remain.

Substitute , and in .

.

Apply logarithm on each side.

gram of the original grams of carbon- will remain in thousand years.

(a) Modeling equation for exponential decay is .

(b) Carbon- will remain after thousand years is grams.

(c) gram of the original grams of carbon - will remain in thousand years.