Math 4b 1. The population of Calfornia was 10,586,223 in 1950 and 23,668,562 in
ID: 2910825 • Letter: M
Question
Math 4b 1. The population of Calfornia was 10,586,223 in 1950 and 23,668,562 in 1980. Assume the population grows exponentially a) Find an exponential function that models the population, P, in terms of t, the years after 1950 b) Use your model, to predict the population of California in 2020. The person drinks a cup of coffee containing 100 mg. of caffeine. The half-life of caffeine in the bloodstream is 6 hours 2. a) Find an exponential function that models the amount of caffeine, C, in terms of t, the hours since the coffee was drank. b) Use your model, to predict how long until only 5 mg. of caffeine remains in the blood stream. 3. A bacteria culture starts with 10,000 bacteria and doubles every 40 minutes. a) Find an exponential function that models the number of bacteria, N, in terms of t, the time in minutes. (HINT: the constant base is NOT 2) b) Use your model, how long until the bacteria populations reaches 1 million. 4 The population of Fresno County was 778615 in 1998 and 909,153 in 2008. Assume the population grows exponentially a) Find a continuous exponential function of the form P-aet that models the population, P, in terms of t, the years after 1998. b) When will the population of Fresno County reach 1 million?. Fact: Neton's Law of Cooling: The temperature difference between an object and the ambient temperature increases/decreases exponentially. That is D aert A hot cup of coffee was brought into a room that was 75* F, the temperature of the cup of tea decrease from 190 F to 120 F in 15 minutes a) Find an continuous exponential function that models the temperature difference, D, in terms of t, the minutes since the tea was brought into the room. b) Use your model, to predict how long until the tea is luke warm (100 F)?Explanation / Answer
1) population in 1950 = 10586223
population in 1980= 23668562
a) exponential model can be written as
P = Po e^kt
23668562 = 10586223 e^30k
k = 0.0268
hence, the function is
P = 10586223 e^.0268t
b) population in 2020
plug t = 70
P = 10586223 e^.0268(70)
P = 69169045.195