Using an exponential equation, supposing a rate of 5%, it is found that it will take about 2.9 years for Emma's balance to reach $450.
An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which:
A(0) is the initial value.
r is the growth rate, as a decimal.
In this problem:
Her initial balance is of $300, hence . A(0)=300
The growth rate is of 15%, hence R =0.15
Then,
[tex]A(t) = A(0)(1+r)^t[/tex]
[tex]A(t) = 300(1+0.15)^t\\A(t) = 300(1.5)^t\\[/tex]
It will reach $450 after t years, for which A(t) = 450, hence:
[tex]A(t) =300(1.15)^t\\450= 300(1.15)^t\\1.15^t=\frac{450}{300}\\\\1.15^t =1.5\\log(1.15)^t=log1.5\\t log 1.15 = log 1.5\\t = \frac{log1.5}{log1.15}\\\\ t =2.9[/tex]
It will take about 2.9 years for Emma's balance to reach $450
Learn more about logarithm here
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