# Determine the algebraic modeling How much money will there be in an account at the end of 7 years if $2000 is deposited at displaystyle{4}% interest compounded serni-annually? # Determine the algebraic modeling How much money will there be in an account at the end of 7 years if$2000 is deposited at displaystyle{4}% interest compounded serni-annually?

Question
Modeling
Determine the algebraic modeling How much money will there be in an account at the end of 7 years if $2000 is deposited at $$\displaystyle{4}\%$$ interest compounded serni-annually? ## Answers (1) 2020-12-14 Given data, $$\displaystyle{t}={7}$$ years $$\displaystyle{P}={2000}$$ $$\displaystyle{|}><={4}\%={0},{04}$$ $$\displaystyle{n}={2}$$ (semi-anually) $$\displaystyle{A}={P}{\left({1}+\frac{{{|}><}}{{n}}\right)}^{t}{n}$$ $$\displaystyle={2000}{\left({1}+\frac{{{0},{04}}}{{2}}\right)}^{{{2}+{7}}}$$ $$\displaystyle={2000}{\left({1}+{0},{02}\right)}^{14}$$ $$\displaystyle={2638},{96}$$ We get a finally answer $$\displaystyle{A}=\{2639}$$ The amoun $$\displaystyle{a}{\mathtt{{|}}}><{7}$$ years is$ 2639

### Relevant Questions

Determine the algebraic modeling If you invest $8,600 in an account paying $$\displaystyle{8},{4}\%$$ annual interest rate, compounded continuously, how much money will be in the account at the end of 11 years? asked 2021-01-19 Determine the algebraic modeling The personnel costs in the city of Greenberg were$9,500,000 in 2009. In the recent past the personnel costs have increased at the rate of $$4.2\%$$ annually.
To model this, the city manager uses the function $$\displaystyle{C}{\left({t}\right)}={9.5}{\left({1}{042}\right)}^{t}\text{where}\ {C}{\left({t}\right)}$$ is the annual personnel costs,in millions of dollars, t years past 2009
1) Write the equation that can be solved to find in what year the personnel costs will be double the 2009 personnel costs.
2) Then solve the equation numerically (use the Table feature of your calculator) or graphically and determine the year.
Determine the algebraic modeling a.
One type of Iodine disintegrates continuously at a constant rate of $$\displaystyle{8.6}\%$$ per day.
Suppose the original amount, $$\displaystyle{P}_{{0}}$$, is 10 grams, and let t be measured in days.
Because the Iodine is decaying continuously at a constant rate, we use the model $$\displaystyle{P}={P}_{{0}}{e}^{k}{t}$$ for the decay equation, where k is the rate of continuous decay.
Using the given information, write the decay equation for this type of Iodine.
b.
Use your equation to determine the half-life ofthis type of Fodine, That is, find ‘out how many days it will take for half of the original amount to be left. Show an algebraic solution using logs.
A car has a purchase price of $24,800. The value declines continuously at an exponential rate of %23 annually. A. Wat is an equation modeling the value of this car after t years? B. What is its value after 6 years? c. How long will it take for its value to be$2000? 2. A bacteria colony grows continuously at an exponential rate. There are initially 1.1 million sent. After 5 days, there are 6.8 million present . a. What is the an equation modeling the number of bacteria present after d days? b. How many bacteria will be present after 7 days? c. How long will it take the number of bacteria to reach 92 million?
A vertical cylinder of cross-sectional area $$\displaystyle{0.050}{m}^{{2}}$$ is fitted with a tight-fitting, frictionless pistionof mass 5.0 kg. If there are 3.0 mol of ideal gas in the cylinderat 500 K, determine the height "h" at which the postion will be inequilibrium.
Trust Fund A philanthropist deposits $5000 in a trust fund that pays 7.5% interest, compounded continuously. The balance will be given to the college from which the philanthropist graduated after the money has earned interest for 50 years. How much will the college receive? asked 2020-11-05 Consider that algebraic modeling Identify the decay factor, if any, for each function. If there is no decay factor, type N. 1) $$\displaystyle{y}={0.8}^{x}$$ 2) $$\displaystyle{y}=-{3}{x}-{8}$$ 3) $$\displaystyle g{{\left({x}\right)}}={\left(\frac{1}{{2}}\right)}^{x}$$ asked 2020-11-08 Testing for a Linear Correlation. In Exercises 13–28, construct a scatterplot, and find the value of the linear correlation coefficient r. Also find the P-value or the critical values of r from Table A-6. Use a significance level of $$\alpha = 0.05$$. Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section 10-2 exercises.) Lemons and Car Crashes Listed below are annual data for various years. The data are weights (metric tons) of lemons imported from Mexico and U.S. car crash fatality rates per 100,000 population [based on data from “The Trouble with QSAR (or How I Learned to Stop Worrying and Embrace Fallacy),” by Stephen Johnson, Journal of Chemical Information and Modeling, Vol. 48, No. 1]. Is there sufficient evidence to conclude that there is a linear correlation between weights of lemon imports from Mexico and U.S. car fatality rates? Do the results suggest that imported lemons cause car fatalities? $$\begin{matrix} \text{Lemon Imports} & 230 & 265 & 358 & 480 & 530\\ \text{Crashe Fatality Rate} & 15.9 & 15.7 & 15.4 & 15.3 & 14.9\\ \end{matrix}$$ asked 2021-02-12 Suppose$10,000 is invested at an annual rate of $$\displaystyle{2.4}\%$$ for 10 years. Find the future value if interest is compounded as follows