Question

A sample of a radioactive isotope had an initial mass of 690 mg in the

year 1997 and decays exponentially over time. A measurement in the
year 2001 found that the sample's mass had decayed to 390 mg. What
would be the expected mass of the sample in the year 2011, to the
nearest whole number?

Answer 1

its 94 on deltamath just did it

Explanation:

Let t=0 represent the year 1997

Starting Value: 690

Write function:

y=690(b)^t

Now find the b-value:

y=390 when t=4 (2001−1997)

390=690(b)^4

390/690=690(b)^4/690

0.56521739=b^4

(0.56521739)^1/4=(b^4)^1/4

0.86706944=b

Write Complete Function:

y=690(0.86706944)^t

Find value in 2011 (use t=14):

y=690(0.86706944)^14

y=93.67062063

y≈94