Question

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?

Answer 1

Answer:

Option A                  

Step-by-step explanation:

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

$f(x) = 18(1.05)^x$    

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

$f(x) = 18(1.05)^x$    

$30 = 18(1.05)^x$    

$\frac{30}{18}=(1.05)^x$    

$1.6666=(1.05)^x$    

Taking log both side and apply property  $logx^a=alogx$  

 $log(1.6666)=xlog(1.05)$  

 $0.221848749616=x0.0211892990699$  

$\frac{0.221848749616}{0.0211892990699}=x$    

$x=10.4698484308$    

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)

                       

Answer 2

we have that

$f(x)=18*(1.05^{x} )$

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