Question

? Question
Emma also wonders how long it will take her balance of $300 to reach $450, assuming she doesn't make
any payments toward it. Write the equation to represent the situation, and solve it using the inverse
relationship between exponential and logarithmic expressions.
Type the correct response in the box. Use numerals instead of words. Round your answer to the nearest
tenth.
It will take about
years for Emma's balance to reach $450.
Part D

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:

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

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

$A(t) = 300(1.15)^t$

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

$A(t) = 300(1.15)^t$

$450 = 300(1.15)^t$

$1.15^t = \frac{450}{300}$

$1.15^t = 1.5$

$\log{(1.15)^t} = \log{1.5}$

$t\log{1.15} = \log{1.5}$

$t = \frac{\log{1.5}}{\log{1.15}}$

$t = 2.9$

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

A similar problem is given at https://brainly.com/question/14773454

Answer 2

Answer:

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