The value of an antique plate after x years can be modeled by f(x) = 18(1.05)x. Which graph can be used to approximate the number of years it will take for the plate’s value to be $30?

Question

contestada

Respuesta :

calculista calculista · Answer 1 · 2018-07-25T20:18:24+02:00

we have that

[tex] f(x)=18*(1.05^{x} ) [/tex]

using a graph tool

see the attached figure N 1

for f(x)=$30

the number of years x is equal

x=10.47 years

the answer in the attached figure N 2

Answer Link

tardymanchester tardymanchester · Answer 2 · 2019-01-18T07:38:58+01:00

Answer:

Option A

Step-by-step explanation:

Given : The value of an antique plate after x years can be modeled by

[tex]f(x) = 18(1.05)^x[/tex]

To find : Which graph can be used to approximate the number of years it will take for the plate’s value to be $30.

Solution: First we find the value of x at y=30

[tex]f(x) = 18(1.05)^x[/tex]

[tex]30 = 18(1.05)^x[/tex]

[tex]\frac{30}{18}=(1.05)^x[/tex]

[tex]1.6666=(1.05)^x[/tex]

Taking log both side and apply property [tex]logx^a=alogx[/tex]

[tex]log(1.6666)=xlog(1.05)[/tex]

[tex]0.221848749616=x0.0211892990699[/tex]

[tex]\frac{0.221848749616}{0.0211892990699}=x[/tex]

[tex]x=10.4698484308[/tex]

Therefore, from the given graph where the value (x,y)=(10.47,30) lie and the curve from (0,18) to (10.47,30) is the solution of the answer.

Hence, option A is correct (also correct graph is attached)