# Chapter 6 Practice Test Group 4 with solutions Chapter 6 ```Q1: Find the general solution to the exact differential equation.
A1: 5^x + tan^-1 + c
Q2: Solve the initial value problem explicitly
A2:
u= x^7- x^3 + 5x + c
Find C
1= 1-1 +5 + c
-5
-5
c= -4
u = x^7 – x^3 + 5x -4
Q3: Euler’s Method with increments of x =0.1 to approximate the value of y when x =
1.3
A3:
(x,y)
dy/dx = x-1
x
(1,2)
(1.1, 2.3)
( 1.2, 3.32)
3
3.2
3.4
.1
.1
.1
2.03
Q4: Find the indefinant integral
A4: t^3/3 + 1/t + c
y= dy/dx (
x)
.3
.32
.34
(x +  x, y +
 y)
(1.1, 2.3)
(1.2, 2.32)
(1.3, 2.03)
Q5: use the indicated substitution to evaluate the integral.
A5: du = 3dx
sin u du/3
1/3 –cos 3x + c
Q6: use substitution to evaluate the integral
A6:
u = 1-x
du= -1
-du=dx
-du/u^2
u^-2 du
u^-1 + c
1/1-x +c
Find the indefinite integral.
1. Q:
A:
2. Q:
A:
3. Q:
A:
Q1: Find the amount of time required for a \$2000 investment to double if the annual
interest rate r is compounded a) annually b) monthly, c) Quarterly and d)
continuously
Q2: An isotope of neptunium has a half-life of 65 minutes. If the decay of this is
modeled by the differential equation dy/dt= -ky, where t is measured in minutes,
what is the decay constant k?
A2:
Q3: The temperature of silver is 60 degrees above room temperature right now.
Twenty minutes ago, it was 70 degrees above room temperature. When will the
silver be 10 degrees above room temp?
Q4: The charcoal from a tree killed in the volcanic eruption that formed crater lake
in Oregon contained 44.5% of carbon-14 found in living matter. About how old is
crater lake?
A4:
Question 1:
A 2000 gallon tank can support no more than 150 guppies. Six guppies are
introduced into the tank. Assume that the rate of growth of the population is:
𝑑𝑃
= 0.0015𝑃 (150 − 𝑃)
𝑑𝑡
a) Find the formula for the guppy population in terms of t.
b) How long will it take for the guppy population to be 125?
Part a: