7:39 PM Sat Mar 21 * 100%| 3. Radioactive decay. Curium-245 has a decay rate of 0.0081547% per year. The rate of change of an amount N of curium-245 after t years is given by dN dt 0.000081547N. a. Let No represent the amount of curium-245 present at t = 0. Find an exponential function that models this situation. b. Suppose 60 mg of curium-245 is present at 1 = 0. How much will remain after 1500 yr? c. What is the rate of change of the amount of curium-245 after 1500 yr? d. After how many years will half of the original 60 mg of curium-245 remain? 4. Radioactive decay. Oxygen-19 has a decay rate of 2.62% per second. The rate of change of an amount N of oxygen-19 after t seconds is given by dN dt 0.0262N. a. Let No represent the amount of oxygen-19 present at t = 0. Find an exponential function that models this situation. b. Suppose 250 mg of oxygen-19 is present at 1 = 0. How much will remain after 1 min? c. What is the rate of change of the amount of oxygen-19 after 1 min? d. After how many seconds will half of the original 250 mg of охygen- 19 remain? e. After how many seconds will 99% of the oxygen-19 have decayed? 5. Radioactive decay. Gold-198 has a decay rate of 25.72% per day. The rate of change of an amount N of gold-198 after t days is given by 0.2572N. dt a. Let No represent the amount of gold-198 present at t = 0. Find an exponential function that models this situation. b. Suppose 10 mg of gold-198 is present at t = 0. How much will remain after 1 week? c. What is the rate of change of the amount of gold-198 after 1 week?
7:39 PM Sat Mar 21 * 100%| 3. Radioactive decay. Curium-245 has a decay rate of 0.0081547% per year. The rate of change of an amount N of curium-245 after t years is given by dN dt 0.000081547N. a. Let No represent the amount of curium-245 present at t = 0. Find an exponential function that models this situation. b. Suppose 60 mg of curium-245 is present at 1 = 0. How much will remain after 1500 yr? c. What is the rate of change of the amount of curium-245 after 1500 yr? d. After how many years will half of the original 60 mg of curium-245 remain? 4. Radioactive decay. Oxygen-19 has a decay rate of 2.62% per second. The rate of change of an amount N of oxygen-19 after t seconds is given by dN dt 0.0262N. a. Let No represent the amount of oxygen-19 present at t = 0. Find an exponential function that models this situation. b. Suppose 250 mg of oxygen-19 is present at 1 = 0. How much will remain after 1 min? c. What is the rate of change of the amount of oxygen-19 after 1 min? d. After how many seconds will half of the original 250 mg of охygen- 19 remain? e. After how many seconds will 99% of the oxygen-19 have decayed? 5. Radioactive decay. Gold-198 has a decay rate of 25.72% per day. The rate of change of an amount N of gold-198 after t days is given by 0.2572N. dt a. Let No represent the amount of gold-198 present at t = 0. Find an exponential function that models this situation. b. Suppose 10 mg of gold-198 is present at t = 0. How much will remain after 1 week? c. What is the rate of change of the amount of gold-198 after 1 week?
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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Transcribed Image Text:7:39 PM Sat Mar 21
* 100%|
3. Radioactive decay. Curium-245 has a decay rate of 0.0081547% per year.
The rate of change of an amount N of curium-245 after t years is given by
dN
dt
0.000081547N.
a. Let No represent the amount of curium-245 present at t = 0. Find an
exponential function that models this situation.
b. Suppose 60 mg of curium-245 is present at 1 = 0. How much will
remain after 1500 yr?
c. What is the rate of change of the amount of curium-245 after 1500
yr?
d. After how many years will half of the original 60 mg of curium-245
remain?
4. Radioactive decay. Oxygen-19 has a decay rate of 2.62% per second. The
rate of change of an amount N of oxygen-19 after t seconds is given by
dN
dt
0.0262N.
a. Let No represent the amount of oxygen-19 present at t = 0. Find an
exponential function that models this situation.
b. Suppose 250 mg of oxygen-19 is present at 1 = 0. How much will
remain after 1 min?
c. What is the rate of change of the amount of oxygen-19 after 1 min?
d. After how many seconds will half of the original 250 mg
of
охygen-
19 remain?
e. After how many seconds will 99% of the oxygen-19 have decayed?
5. Radioactive decay. Gold-198 has a decay rate of 25.72% per day. The rate of
change of an amount N of gold-198 after t days is given by
0.2572N.
dt
a. Let No represent the amount of gold-198 present at t = 0. Find an
exponential function that models this situation.
b. Suppose 10 mg of gold-198 is present at t = 0. How much will
remain after 1 week?
c. What is the rate of change of the amount of gold-198 after 1 week?
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