Question

Emma also wonders how long it will take her balance of $300 to reach $450, assuming she doesn't make any payments

Answer 1

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:

$A(t) = A(0)(1+r)^t$

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,

$A(t) = A(0)(1+r)^t$

$A(t) = 300(1+0.15)^t\\A(t) = 300(1.5)^t$

It will reach $450 after t years, for which A(t) = 450, hence:

$A(t) =300(1.15)^t\\450= 300(1.15)^t\\1.15^t=\frac{450}{300}\\\\1.15^t =1.5\\log(1.15)^t=log1.5\\t log 1.15 = log 1.5\\t = \frac{log1.5}{log1.15}\\\\ t =2.9$

It will take about 2.9 years for Emma's balance to reach $450

Learn more about logarithm here

brainly.com/question/247340

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