Chapter 8

Question 1

What is true for all graphs of y = a^x?

Answer 1

.y-intercept - (0,1).
.Above x-axis.
.Asymptote at x-axis.
.Exponential growth - a > 1.
.Exponential decay - 0 < a < 1.

Question 2

What is the gradient of e^x?

Answer 2

e^x.

Question 3

What is the gradient of e^kx?

Answer 3

ke^kx.

Question 4

a^x written as e^kx shows exponential growth when:

Answer 4

.a > 1.
.k is positive.

Question 5

a^x written as e^kx shows exponential decay when:

Answer 5

.a < 1.
.k is negative.

Question 6

What are the key points of the graph y = ln(x)?

Answer 6

.Passes through (0,1).
.Vertical asymptote at y-axis.

Question 7

What does this show about the rate of change?

Answer 7

Proportional to the quantity itself.

Question 8

What is the initial value of y = Ae^kt?

Answer 8

t = 0 so A.

Question 9

What is the rate of growth of y = Ae^kt?

Answer 9

ky = kAe^kt.

Question 10

What is the data for y = kb^x?

Answer 10

.log y = log k + xlog b
.log y against x.
.m - log b.
.c - log k.

Question 11

What is the data for y = ax^n?

Answer 11

.log y = log a + nlog x.
.log y against log x.
.m - n.
.c - log a.