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 [tex]\[3,500(1.003)^{t}\][/tex]
We need to determine the value of t when f(t)>=3700
Expressing it in equation form,
[tex]\[3,500(1.003)^{t} >= 3700\][/tex]
[tex]\[=>(1.003)^{t} >= \frac{3700}{3500}\][/tex]
[tex]\[=>(1.003)^{t} >= 1.057\][/tex]
Taking log of both sides,
[tex]\[=>t * log(1.003) >= log(1.057)\][/tex]
[tex]\[=>t >= \frac{log(1.057)}{log(1.003)}\][/tex]
[tex]\[=>t >= 18.51\][/tex]
So t = 19.
