Exponential Growth and Decay: Word Problems
Dr. Vega is contemplating the impact of an antibiotic on a particular patient. The patient will take 98 milligrams, and every hour his body will break down 34.6% of it. How much will be left after 6 hours?
What is 7.7 milligrams?
Factor.
z2- 14z–32
What is (z + 2)(z - 16)?
Find g(x), where g(x) is the translation 5 units left and 5 units up of f(x) = x2
What is g(x) = (x + 5)2 + 5?
Line segment AB has an endpoint, A, located at (10,−1), and a midpoint at (10,0). What are the coordinates for point B of segment AB?
What is (10, 1)?
What does the transformation f(x) ↦ f (1/3 x) do to the graph of f(x)?
Stretches it horizontally
Marvin has a vintage comic book worth $351. According to a dealer, the value of this particular comic book will increase by 12.1% each year. How much will the comic book be worth in 13 years?
What is $1,549.46?
Factor.
v2+ 11v – 42
What is (v - 3)(v + 14)?
Find g(x), where g(x) is the translation 10 units left and 4 units down of f(x) = x2
What is g(x) = (x + 10)2 - 4?
A line segment has endpoints (0,4) and (5,6). What are the coordinates of the midpoint?
What is (2.5 , 5)?
What does the transformation f(x) ↦ 1/2 f(x) do to the graph of f(x)?
Shrinks it vertically
An art gallery owns a sculpture that is valued at $34,055. The gallery owner estimates that its value will increase by 6% every year. If the owner is correct, then how much will it be worth in 15 years?
What is $81,614.79?
Factor.
u2 – 2u – 15
What is (u + 3)(u - 5)?
Find g(x), where g(x) is the translation 4 units left and 4 units up of f(x)= x2
What is g(x) = (x + 4)2 + 4?
What is the midpoint between (1,4) and (5,12)?
What is (3, 8)?
What does the transformation f(x) ↦ f(x + 9)– 9 do to the graph of f(x)?
Translates 9 units left and 9 units down.
You have 979,584 grams of a radioactive kind of argon. If its half-life is 2 hours, how much will be left after 10 hours?
What is 30,612 grams?
Factor.
w2 + 16w – 17
What is (w - 1)(w + 17)
Find g(x), where g(x) is the translation 1 unit left and 1 unit up of f(x)= x2
What is g(x) = (x + 1)2 + 1?
A line segment connects the points (−1,4) and (3,16). What is the midpoint of this segment?
What is (1, 10)?
What does the transformation f(x) ↦ 1/7 f(x) do to the graph of f(x)?
Shrinks it vertically
How much of a radioactive kind of tellurium will be left after 12 months if the half-life is 2 months and you start with 864,640 grams?
What is 13,510 grams?
Factor.
s2 – 5s – 14
What is (s + 2)(s - 7)?
Find g(x), where g(x) is the translation 8 units left of f(x)= x2
What is g(x) = (x + 8)2 ?
What is the midpoint between the points (–1, 2) and (3, –6)?
What is (1, -2)?
What does the transformation f(x) ↦ f(x) + 4 do to the graph of f(x)?
Translates it 4 units up