Question

2.c is anyone good with exponential and logarithmic?

Answer 1

After 48 months the value will increase by 10 percent of the initial value.

Explanation:

Let's first find the rate of increase for each period which is 3 months here.

According to the table at month
`x=0` value is
`2000`dollars and at month
`x=3` value is
`2012`dollars.

∴
`2012=2000(1+(r)/(100) )^1`

⇒
`1+(r)/(100) =(2012)/(2000)=1.006`

⇒
`r=0.006*100`

⇒
`r=0.6`%

Now the question is to find how long it will take for the investment value to increase 10 percent.

`y=2000(1+0.006)^(x)/(3)`

`2000(1+0.1)=2000(1.006)^(x)/(3)`

⇒
`(1.006)^(x)/(3) =1.1`

⇒
`(x)/(3)=(log(1.1))/(log(1.006))`

⇒
`x=3((log(1.1))/(log(1.006)) )`

⇒
`x=47.7979126....`

∴at
`x=48` the value will slightly cross 10 percent increase.