The value of a car is V(x)= 10(.75)x, where x≥0 is the age of the car in years and V(x) is its value in thousands of $.
Rewrite the function using a rational number instead of the decimal. Is it an increasing or decreasing function? What is the starting value of the car? Evaluate:
Solve: V(x)=10 x= V(x)=5 x= V(x)=2.5 x= V(x)=1.25 x=
Based on these, how much time does it take for the value of the car to halve?
Graph the function. What is the y-intercept?
The price of a stock of MEGA Corp. is P(x)= 10(1.25)x, where x≥0 is the numbers of years from today and P(x) is the stock's price in $.
Is it an increasing or decreasing function? What is the starting value of the stock? Evaluate: P(0) = P(1) = P(2) = P(3) = P(5) = P(10) = P(20) =
Solve: P(x)=10 x= P(x)=20 x= P(x)=40 x= P(x)=80 x=
Based on these, how much time does it take for the price of the stock to double? Graph the function. What is the y-intercept?
Some 60°C warm stuff is put into a 10°C cool place. Its temperature T after t minutes is T(t)= 10 + 50e-0.1t
Is it an increasing or decreasing function?
Evaluate: T(0) = T(1) = T(2) = T(5) = T(10) = T(20) = T(30) = T(50) =
What looks to be the horizontal asymptote as t gets large?
Solve: T(t)=60 t= T(t)=50 t= T(t)=40 t= T(t)=30 t= T(t)=20 t= T(t)=15 t= T(t)=11 t= T(t)=10.5 t= T(t)=10.1 t= T(t)=10.01 t= T(t)=10 t=
World population doubled in the 40 years between 1960 and 2000, from 3 billion to 6 billion. From this fact, a function that predicts future world population, in billions, is: WP(t)= 6·20.025t where t is years since 2000.
Evaluate: If this trend continues (it hasn't but pretend it did), what should the world population be in 2024? = in 2000? = in 2050? = in 2100? =
Solve: When will the world population be 10 billion? WP(t)=10 year= 6 billion? WP(t)=6 year= 100 billion? WP(t)=100 year=
Carbon-14 is radioactive, which means some random atoms of a clump of it will change to some other kind of atom at a known rate. Half of it will have changed in 5730 years (its "half-life"). The decimal percent amount of the starting pile that still is carbon-14 after t years is: S(t)= e-0.000121t
Evaluate: How much (what percent) is still carbon-14 after 0 years: S(0) = 1000 years: S(1000) = 2000 years: S(2000) = 10000 years: S(10000) = 20000 years: S(20000) = 100000 years: S(100000) =
Solve: How many years for there to be one half of the starting amount: S(t)=.5 t= How many years for there to be one quarter of the starting amount: S(t)=.25 t= How many years for there to be one eighth of the starting amount: S(t)=.125 t= How many years for there to be one sixteenth of the starting amount: S(t)=.0625 t= Based on these, how much time does it take for the amount to halve? t=
Graph the function. Adjust the axes to see the decreasing exponential curve.