Survey of calculus : MTH 124 practice sets answers

The following functions give the populations of four towns with time t in years. A. P=650(0.9)t B. P=830(1.08)t C. P=240(1.12)t D. P=1040(1.04)t (a) Which town has the fastest rate of growth? What is the rate of growth? (b) Which town has the largest initial population? What is that initial population? (c) Which town(s) are decreasing in size?

(a) The town C has the largest growth rate = 1.12 (b)The town D has the largest initial population = 1040 (c) A. P=650(0.9)t .

Solve the exponential equation. Express the solution as an exact answer in terms of natural logarithms. Then use a calculator to give an approximation of the solution, rounded to two decimal places. e^9−4x=6562

(ln(6562)-9)/-4

Use the quadratic formula to solve the quadratic equation 2x2−2x−5=0.

-1.158, 2.158

One of the main contaminants of a nuclear accident, such as that at Chernobyl, is strontium-90, which decays exponentially at an annual rate of approximately 2.7% per year. (a)Write the percent of strontium-90 remaining,P, as a function of years,t, since the nuclear accident. Answer: P= Estimate the half-life of strontium-90. Answer: t= After the Chernobyl disaster, it was predicted that the region would not be safe for human habitation for 97 years. Estimate the percent of original strontium-90 remaining at this time. Answer:

100(0.973)^t 25.32 years 7.03%

A bird species in danger of extinction has a population that is decreasing exponentially (A=A0ekt). 77 years ago the population was at 1760 and today only 1130 of the birds are alive. Once the population drops below 220, the situation will be irreversible. When will this happen? HINT: find k first

26 years

The half-life of a certain substance is 14.5 years. Suppose that today you have 285 How much will be left after 29 years? How much will be left after 43.5 years? How much will be left after 59 years?

71.25 35.63 16.98

use the exponential decay model for carbon-14, A=A0e−0.000121t, to solve this exercise. Some cave paintings were discovered today in a cave in South Carolina. The paint contained 41%41% of the original carbon-14. Estimate the age of the paintings. ANSWER: The paintings are approximately

7370 years old

The gross domestic product, G, of Switzerland was 260 billion dollars in 2007. Give a formula for G (in billions of dollars) t years after 2007 if G increases by (a) 2.7% per year. b)7 billion dollars per year.

Answer: G(t)= 260(1+.027)^t 7 billion dollars per year. Answer: G(t)= 260+7t

Let C=f(t) represent winter wheat production in Ontario in thousands of tons, where tt is years since 1980. Interpret the statement f(1)=707:

In the year 1981 , Ontario produced 707 thousands of tons of winter wheat.

CFC-11 is a chlorofluorocarbon which has been widely used in refrigerants and in the blowing of foam, and which is known to have a damaging effect on the environment. Emissions of CFC-11 have declined since the enactment of the 1987 Montreal Protocol. Global emissions C=f(t) of CFC-11, in thousands of tons, is a function of time, t, in years since 1987. (a) Interpret the statement f(4)=219:

In the year 1991 , global emissions of CFC-11 were measured to be 219 thousands of tons.

Let y=f(x)=5x2+9y (a) Find the value of y when x is zero. Answer: y . (b) What is f(2)f(2)? Answer: f(2)r . (c) What value(s) of x give y the value of 14? Answer: x=. (d) What value(s) of x give y the value of 88? Answer: x=

a)9 b)29 c)1. -1 d)none

Solve for t using natural logarithms. Express the solution as an exact answer in terms of natural logarithms. (a)29=90e−0.04t (b) B=Pert 2e8t=7e7t

ln(29/90)/-0.04 ln(B/P)/r ln(7/2)