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

Explanation:

From the given formula,

`P(t)=P(0)e^(rt)`

`(P(t))/(P(0))=e^(rt)`

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

`\text{ln}[(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}[(984)/(800)]=5r`

r =
`(0.207)/(5)`

r ≈ 4.2%

2).
`\text{ln}[(1464)/(1200)]=4r`

r =
`(0.19885)/(4)`

r = 0.0497

r = 5%

3).
`\text{ln}[(1111.5)/(950)]=0.045t`

t =
`(0.157)/(0.045)`

t = 3.5 years

4).
`\text{ln}[(775)/(620)]=3.7t`

t =
`(0.22314)/(0.037)`

t ≈ 6 years

5).
`\text{ln}[(1066.8)/(840)]=8r`

r =
`(0.239)/(8)`

r ≈ 3%