Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The exponential function
h is graphed in the
xy-plane. If the graph contains the points
(0,18) and
(4,3), which of the following could be
h ?
Choose 1 answer:
(A)
h(x)=16((1)/(2))^(x)+2
(B)
h(x)=16((1)/(2))^(x)+3
(c)
h(x)=18((1)/(3))^((x)/(2))
(D)
h(x)=18((1)/(2))^(x)-2

The exponential function $h$ is graphed in the $x y$ -plane. If the graph contains the points $(0,18)$ and $(4,3)$ , which of the following could be $h$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $h(x)=16\left(\frac{1}{2}\right)^{x}+2$ $\newline$ (B) $h(x)=16\left(\frac{1}{2}\right)^{x}+3$ $\newline$ (C) $h(x)=18\left(\frac{1}{3}\right)^{\frac{x}{2}}$ $\newline$ (D) $h(x)=18\left(\frac{1}{2}\right)^{x}-2$

View step-by-step help

View step-by-step help

Compare linear and exponential growth

Full solution

Q. The exponential function

h

is graphed in the

x y

-plane. If the graph contains the points

(0,18)

and

(4,3)

, which of the following could be

h

?

\newline

Choose

1

answer:

\newline

(A)

h(x)=16\left(\frac{1}{2}\right)^{x}+2

\newline

(B)

h(x)=16\left(\frac{1}{2}\right)^{x}+3

\newline

(C)

h(x)=18\left(\frac{1}{3}\right)^{\frac{x}{2}}

\newline

(D)

h(x)=18\left(\frac{1}{2}\right)^{x}-2

Test option (A) with $(0,18)$ : We will test each function option by plugging in the given points to see if they satisfy the function. $\newline$ First, let's test option (A) with the point $(0,18)$ . $\newline$ $h(x) = 16(\frac{1}{2})^x + 2$ $\newline$ $h(0) = 16(\frac{1}{2})^0 + 2$ $\newline$ $h(0) = 16(1) + 2$ $\newline$ $h(0) = 16 + 2$ $\newline$ $h(0) = 18$
Test option (A) with $(4,3)$ : Now let's test option (A) with the point $(4,3)$ . $h(4) = 16(\frac{1}{2})^4 + 2$ $h(4) = 16(\frac{1}{16}) + 2$ $h(4) = 1 + 2$ $h(4) = 3$
Option (A) satisfies both points: Since option (A) satisfies both points $(0,18)$ and $(4,3)$ , we have found a function that could represent $h$ . We do not need to test the other options because the question asks for ＂which of the following could be $h$ ＂ and not ＂which of the following are all possible $h$ ＂.

More problems from Compare linear and exponential growth

Question

Jill bought a used motorcycle from a seller online for $1,200. The seller will charge her $5 a day to store the motorcycle at his house until she is able to pick it up. You can use a function to describe the total amount of money Jill will owe the seller if she waits

x

days to pick up the motorcycle.

\newline

Write an equation for the function. If it is linear, write it in the form

g(x) = mx + b

. If it is exponential, write it in the form

g(x) = a(b)^x

\newline

g(x) = \underline{\hspace{3em}}

Posted 5 months ago

Question

f(t)=-2t-7

change over the interval from

t=-7

t=-6

\newline

\newline

\left[\text{f(t) decreases by } 2\right]

\newline

\left[\text{f(t) increases by } 2\right]

\newline

\left[\text{f(t) increases by } 200\%\right]

\newline

\left[\text{f(t) decreases by a factor of } 2\right]

Posted 5 months ago

Question

g(t)=9^t

change over the interval from

t=1

t=3

\newline

\newline

\left[\text{g(t) decreases by a factor of } 81\right]

\newline

\left[\text{g(t) increases by a factor of } 81\right]

\newline

\left[\text{g(t) increases by } 18\%\right]

\newline

\left[\text{g(t) decreases by } 9\%\right]

Posted 5 months ago

Question

Both of these functions grow as

x

gets larger and larger. Which function eventually exceeds the other?

\newline

\newline

(A)f(x) = 8x + 3.3

\newline

(B)g(x) = 3.3^x - 5

Posted 6 months ago

Question

Both of these functions grow as

x

gets larger and larger. Which function eventually exceeds the other?

\newline

\newline

(A) \ f(x) = 2x + 9

\newline

(B)\ g(x) = 2^x

Posted 6 months ago

Question

f(x)

g(x)

are differentiable.

\newline

h(x)

h(x)=\frac{g(x)}{f(x)}

\newline

f(8)=1

f'(8)=-6

g(8)=8

g'(8)=-10

h'(8)

\newline

Simplify any fractions.

\newline

h'(8)=

Posted 6 months ago

Question

p(x)

q(x)

are differentiable.

\newline

r(x)

r(x)= \frac{p(x)}{q(x)}

\newline

p(3)= 2

p'(3)= 4

q(3)= 6

q'(3)= 9

r'(3)

\newline

Simplify any fractions.

\newline

r'(3)=

Posted 7 months ago

Question

u(x)

v(x)

are differentiable.

\newline

w(x)

w(x)= \frac{u(x)}{v(x)}

\newline

u(5)= 3

u'(5)= -2

v(5)= 7

v'(5)= 1

w'(5)

\newline

Simplify any fractions.

\newline

w'(5)=

Posted 7 months ago

Question

a(x)

b(x)

are differentiable.

\newline

c(x)

c(x)= \frac{a(x)}{b(x)}

\newline

a(2)= 4

a'(2)= 5

b(2)= 1

b'(2)= -3

c'(2)

\newline

Simplify any fractions.

\newline

c'(2)=

Posted 7 months ago

Question

m(x)

n(x)

are differentiable.

\newline

o(x)

o(x)= \frac{m(x)}{n(x)}

\newline

m(7)= 2

m'(7)= -1

n(7)= 4

n'(7)= 8

o'(7)

\newline

Simplify any fractions.

\newline

o'(7)=

Posted 7 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant