Calculus Chapter 1

The half-life of radioactive strontium-90 is approximately 28 years. In 1960, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's bones. How many years does it take until only 12 percent of the original amount absorbed remains?

(-28*ln(.12))/(ln(2))

A pomegranate is thrown from ground level straight up into the air at time t=0 with velocity 160 feet per second. Its height in feet at t seconds is f(t)=-16 t^2+160 t. Find the time its hits the ground and the time it reaches its highest point. (a) Hits the ground when t= (b) Reaches highest point when t= (c) Maximum height =

(a) (b) (c)

A town has a population of 1600 people at time t=0. In each of the following cases, write a formula for the population P, of the town as a function of year t. (a) The population increases by 70 people per year. (b) The population increases by 9 percent a year.

(a) 1600+70t (b) 1600(1+.09)^t

The monthly charge for a waste collection service is 2025 dollars for 100 kg of waste and 2925 dollars for 145 kg of waste. (a) Find a linear model for the cost, C, of waste collection as a function of the number of kilograms, w. (b) What is the slope of the line found in part (a)? (c) What is the value of the vertical intercept of the line found in part (a)?

(a) 20w+25 (b) 20 (c) 25

Find a formula for the graph of the function y = f(x) given in the figure above. y =

-cos(x)+4

Find a formula for the graph of the function f(x) given in the figure above. f(x)=

-sin((pi/4pi)x)

Find the equation for a cubic polynomial that could generate this graph given that it passes through the point (0,4).

-x(x-4)^2

The figure above is the graph of an invertible function f(x). Use the figure to find the following: 1) f^{-1} (-5)= 2) f^{-1} (-4)= 3) f^{-1} (-3)=

1) -6 2) -3 3) 2

The figure above is the graph of the function m(t). Let n(t)=m(t)+2, k(t)=m(t+1.5),w(t)=m(t-0.5)-2.5 and p(t)=m(t-1). Find the values of the following: 1) n(-2.5)= 2) n(1)= 3) k(1.5)= 4) w(2.5)= 5) w(0.5)= 6) p(2)=

1) 1 2) 7 3) 5 4) .5 5) .5 6) 5

Find the equation of the line that passes through the (x,y) points (0 ,1 ) and (1 ,6 ).

5x+1

Put the function P=25 (3.1)^{t} in the form P_{0} e^{kt}. When written in this form, you have: k = p₀ =

k = ln3.5 p₀ = 25

Solve for x: 4 e^{4 x} = 7 e^{5 x}

ln/((ln7)*(5/4))

Solve the equation (x + 5)^2 + 6 = 70. If there is more than one correct answer, enter your answers as a comma separated list. x =

x = 3,-13