Question

2.c is anyone good with exponential and logarithmic?

Answer 1

Answer:

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

Step-by-step 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.

∴$2012=2000(1+\frac{r}{100} )^1$

⇒$1+\frac{r}{100} =\frac{2012}{2000}=1.006$

⇒$r=0.006*100$

⇒$r=0.6$%

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

$y=2000(1+0.006)^\frac{x}{3}$

$2000(1+0.1)=2000(1.006)^\frac{x}{3}$

⇒$(1.006)^\frac{x}{3} =1.1$

⇒$\frac{x}{3}=\frac{log(1.1)}{log(1.006)}$

⇒$x=3(\frac{log(1.1)}{log(1.006)} )$

⇒$x=47.7979126....$

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