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ArbitrLikvidat [17]
3 years ago
9

Natalie has $5000 and decides to put her money in the bank in an account that has a 10% interest rate that is compounded continu

ously.
What type of exponential model is Natalie’s situation?
Write the model equation for Natalie’s situation
How much money will Natalie have after 2 years?
How much money will Natalie have after 10 years?
Mathematics
1 answer:
kakasveta [241]3 years ago
5 0

Step-by-step explanation:

  • Natalie has $5000
  • She decides to put her money in the bank in an account that has a 10% interest rate that is compounded continuously.

Part a) What type of exponential model is Natalie’s situation?

Answer:

As Natalie's situation implies

  • continuous compounding. So, instead of computing interest on a finite number of time periods, for instance monthly or yearly, continuous compounding computes interest assuming constant compounding over an infinite number of periods.

So, it requires the more generalized version of the principal calculation formula such as:

P\left(t\right)=P_0\times \left[1+\left(i\:/\:n\right)\right]^{\left(n\:\times \:\:t\right)}

or

P\left(t\right)=P_0\times \left[1+\left(\frac{i}{n}\:\right)\right]^{\left(n\:\times \:\:t\right)}

Here,

i = interest rate

= number of compounding periods

t = time period in years

Part b) Write the model equation for Natalie’s situation?

For continuous compounding the number of compounding periods, n, becomes infinitely large.

Therefore, the formula as we discussed above would become:

                                        P\left(t\right)=P_0\times e^{\left(i\:\times \:t\right)}

Part c) How much money will Natalie have after 2 years?

Using the formula

                            P\left(t\right)=P_0\times e^{\left(i\:\times \:t\right)}

$₂ =\:6107.02 $

So, Natalie will have \:6107.02 $ after 2 years.

Part d) How much money will Natalie have after 2 years?

Using the formula

                            P\left(t\right)=P_0\times e^{\left(i\:\times \:t\right)}

$₁₀ =13.597.50 $

So, Natalie will have 13.597.50 $ after 10 years.

Keywords: word problem, interest

Learn more about compound interest from brainly.com/question/6869962

#learnwithBrainly

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Step-by-step explanation:

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Equation at the end of step  1  :

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Step  2  :

Solving a Single Variable Equation :

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Two solutions were found :

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Not sure what you need help with, but I hope I helped you somehow.

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First we can by -3 in both sides of the inequality, and remember, because we are multiplying by a negative number, the inequality sign changes its direction:

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Now we can subtract 1 in both sides:

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