Calculus 2 Exponential Growth and Decay

1. In the chemical reaction called the inversion of raw sugar,
the inversion rate is proportional to the amount of raw sugar
remaining. If 100 kg of raw sugar is reduced to 75 kg in 6 hours,
how long will it be until:

a. half the raw sugar has been inverted?

b. 90% of the raw sugar has been inverted?

2. If 100 g of a radioactive substance is reduced to 40 g in 6
hours and if the decay is exponential, what is the half-life?

3. Scientists who do carbon-14 dating use 5730 years for the
half-life of carbon-14. A specimen of charcoal found at Stonehenge
contains 63% as much Carbon-14 as a sample of present-day charcoal.
What is the age of the sample?

4. In 1950 the total number of physicians in the United States
was 219,997. In 2000 it was 813,869. Assuming the exponential model
applies, estimate the number of physicians in the United States in
2025 and 2050.