IDNLearn.com: Your trusted source for finding accurate answers. Our community provides timely and precise responses to help you understand and solve any issue you face.

From the list below, indicate which exponential function represents an increasing function. Select all that apply.• h (x)=7(0.9)^x• k (x)=10(3/5)^x• n (x)=4(7/6)^x• p (x)= -10(8)^x• j (x)=2(1+0.03)^x• g (x)=0.25×6^x• f (x)=5×2^x• m (x)=3(4)^x -5

Sagot :

Exponential functions

Initial explanation

An exponential function is given by the formula:

[tex]f(x)=a\cdot b^x[/tex]

where a and b are numbers. b is always positive

We have that there are two ways of obtaining a decreasing exponential function:

1. if a is negative

2. if 0 < b < 1

We have that we have an increasing function if and only if

a is positive and b is higher than 1, b > 1

Analysis

We have that:

In h(x) = 7 · 0.9ˣ

a = 7 and b = 0.9

Since 0 < 0.9 < 1, then it is a decreasing function.

In k(x) = 10 · (3/5)ˣ

a = 10 and b = 3/5 = 0.6

Since 0 < 3/5 < 1, then it is a decreasing function.

In n(x) = 4 · (7/6)ˣ

a = 4 and b = 7/6 = 1.166...

Since a is positive and b is higher than 1: 1 < 1.166...,

then it is an increasing function.

In p(x) = -10 · 8ˣ

a = -10 and b = 8

Since a is negative, then it is a decreasing function.

In j(x) = 2 · (1 + 0.03)ˣ

a = 2 and b = 1 + 0.03 = 1.03

Since a is positive and b is higher than 1: 1 < 1.03,

then it is an increasing function.

In g(x) = 0.25 · 6ˣ

a = 0.25 and b = 6

Since a is positive and b is higher than 1: 1 < 6,

then it is an increasing function.

In f(x) = 5 · 2ˣ

a = 5 and b = 2

Since a is positive and b is higher than 1: 1 < 2,

then it is an increasing function.

In m(x) = 3 · 4ˣ - 5

a = 3 and b = 4

Since a is positive and b is higher than 1: 1 < 4,

then it is an increasing function.

Answer- the increasing functions are:

View image LeonoreY636235
View image LeonoreY636235
View image LeonoreY636235
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. For precise answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.