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

Answer:

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

Step-by-step 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,

$\[3,500(1.003)^{t} >= 3700\]$

$\[=>(1.003)^{t} >= \frac{3700}{3500}\]$

$\[=>(1.003)^{t} >= 1.057\]$

Taking log of both sides,

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

$\[=>t >= \frac{log(1.057)}{log(1.003)}\]$

$\[=>t >= 18.51\]$

So t = 19.