7.4 Exponential Decay Modeling

If a radioactive substance is quickly decaying at a rate of 13% per hour, approximately how much of a 200 pound sample remains after one day?

• 7.1 pounds

• 2.3 pounds

• 25.6 pounds

• 15.6 pounds

Answer explanation

A population of Llamas stranded on a desert island is decreasing due to a food shortage by 6% per year. If the population of Llamas started out at 350, how many are left on the island 10 years later?

• 257

• 58

• 102

• 189

When the world market is glutted with oil, its price per barrel can drop as much as 5% per day. If the per barrel price of oil starts at the beginning of the week with a value of $120 and loses 5% per day, how much value will it lose over the span of 5 days?

• $92.85

• $54.75

• $27.15

• $32.80

Answer explanation

The acceleration of an object falling through the air will decrease at a rate of 15% per second due to air resistance. If the initial acceleration due to gravity is 9.8 meters per second, which of the following equations best models the acceleration t seconds after the object begins falling?

• $a=15\times9.8t^{2\ }$

• $a=\frac{9.8}{15t}$

• $a=9.8\left(1.15\right)^t$

• $a=9.8\left(0.85\right)^t$

A radioactive substance loses 1.5% of its mass every year that it decays. Which of the following is closest to its half-life in years?

• 58

• 46

• 215

• 3176

Answer explanation

A warm glass of water is placed in a refrigerator at 34 degrees F, and its temperature is seen to decrease according to the exponential function:

 $T=86\left(0.83\right)^t+34$  

What was the initial temperature of the water, in degrees F? Do not use units in your answer.

(a)  

Answer explanation