Question

Use the formula Pt= P0e^rt. where Pt is the amount after t years, P0 is the initial amount, t is the rate of interest, and t is the time period, to complete the table.

Answer 1

Answer:

Step-by-step explanation:

From the given formula,

$P(t)=P(0)e^{rt}$

$\frac{P(t)}{P(0)}=e^{rt}$

$\text{ln}[\frac{P(t)}{P(0)}]=\text{ln}[e^{rt}]$

$\text{ln}[\frac{P(t)}{P(0)}]=rt$

Now we put the values in the formula to get the values of the blank spaces in the table,

1). $\text{ln}[\frac{984}{800}]=5r$

   r = $\frac{0.207}{5}$

   r ≈ 4.2%

2). $\text{ln}[\frac{1464}{1200}]=4r$

   r = $\frac{0.19885}{4}$

   r = 0.0497

   r = 5%

3). $\text{ln}[\frac{1111.5}{950}]=0.045t$

   t = $\frac{0.157}{0.045}$

   t = 3.5 years

4). $\text{ln}[\frac{775}{620}]=3.7t$

   t = $\frac{0.22314}{0.037}$

   t ≈ 6 years

5). $\text{ln}[\frac{1066.8}{840}]=8r$

   r = $\frac{0.239}{8}$

   r ≈ 3%