Question

the function f(t)= 3,500(1.003)^t gives the value of a saving account t months after it was opened.How long will it take for the account balance to refresh $3,700? Round to the nearest whole number.

Answer 1

After 19 months,value in the account will reach $3700

Explanation:

The value of a savings account f(t) in terms of t ( number of months since account opening) is given as
`\[3,500(1.003)^(t)\]`

We need to determine the value of t when f(t)>=3700

Expressing it in equation form,

`\[3,500(1.003)^(t) >= 3700\]`

`\[=>(1.003)^(t) >= (3700)/(3500)\]`

`\[=>(1.003)^(t) >= 1.057\]`

Taking log of both sides,

`\[=>t * log(1.003) >= log(1.057)\]`

`\[=>t >= (log(1.057))/(log(1.003))\]`

`\[=>t >= 18.51\]`

So t = 19.