Question

A toxic radioactive substance with a density of 8 milligrams per square centimeter is detected in the ventilating ducts of a nuclear processing building that was used 35 years ago.

The density of the radioactive substance when it was deposited 35 years ago was approximately _ mg/cm

Between 2005 and 2009, the average rate of inflation was about 2.8% per year. If a cart of groceries cost $180 in 2005, what did it cost in 2009?

A cart of groceries cost approximately $_ in 2009. (Round to the nearest two decimal places as needed)

Suppose your dog weighs 3.5 pounds at birth and weighed 15.2 pounds one year later. Based on these two data points,find a linear function that describes how weight varies with age. Use this function to predict your dog's weight at four and ten years of age. comment on the validity of this model.

The equation used to model this situation is _ where the W is the weight of the dog in pounds and t is the time in years.

Answer 1

Solution :- O given data is densidy = 8 mg / cm² that is used 35 yeau ago %3D y (35) => 0:5 (: Subslance getting halved) M = 50%- Now, Joumula fou decay is givem by a (i-4)*. ylt) Let the halt life of the Now, Subs dauce is 20 year So we get 35 35 20 %3D 1.75 Now Putting y(t) = 8 get we al1-0-5)75 8. 26.85 (0.5) 1" 1.75 0-298 26.85 2 mg/cm densi dy of eadioa chive Substance when it So, the was defesited 35 yeau ago was appuoximatly 26.85 mg/ cm?.

Soludion :- 2 given data is guocunies Cost ce) = $ 180 0.028 4= 2.8%. Mate 4 yeau. Hime fuom 2005 - 2009 we haue to Jend Cost in 200 9 the Joumula - using haue to Jeñd A (accumula ted amount) A = P(I+ u) 80(1+0.028) 1 201.02 180 (1-028) 180x 1.12 $201.02 so, the Caut g quoceuies Cost appuoximatly $ 201.02 in 2009. Soluhion:- 3 given data is at > weight 1 year age 3 weight 3.5 pounds age at 15.2 pound two poinds) (0, 3:5) and (1g 15.2) ( shese aue a lineau W = mt + b nctron is puf of ) Jending Slope m g the Heue we have and b Equadion

92-41 15.2-3.5 %3D 11.7 %3D using fiest point (o, 3-5) Jind NOLO ) we mt +b -> 3.5 = m(0) b=3.5 So, linear NOLO haue m = 1|•7 b= 3.5 we Junction is : - Heue weight w is 11.7t + 3.5 is time. Now, finding dog's weight at 11.7X 4 + 3•5 50.3 Pounds %3D dog's weight at Now, t =10 11.7X10+ 3•5 120-5 Pounds. > ie dog's weight at age of 120.5 Pounds year this model is not uealistc because many dogs 10 guow fasted Hence in life. gain weight Jassero eauy