# Exponential models questions and answers

Recent questions in Exponential models
Exponential models

### For the following exercises, consider this scenario: For each year t, the population of a forest of trees is represented by the function $$A(t)=115(1.025)^t$$. In a neighboring forest, the population of the same type of tree is represented by the function $$\displaystyle{B}{\left({t}\right)}={82}{\left({1.029}\right)}^{{t}}$$. (Round answers to the nearest whole number.) Discuss the above results from the previous four exercises. Assuming the population growth models continue to represent the growth of the forests, which forest will have the greater number of trees in the long run? Why? What are some factors that might influence the long-term validity of the exponential growth model?

Exponential models

### The exponential models describe the population of the indicated country. A, in millions, t years after 2006. Which country has the greates growth rate? By what percentage is the population of that country increasing each year? Country1: $$\displaystyle{A}={129.3}{e}^{{{0.001}{t}}}$$ Country 2: $$\displaystyle{A}={1096.9}{e}^{{{0.011}{t}}}$$ Country 3: $$\displaystyle{A}={28.7}{e}^{{{0.028}{t}}}$$ Country 3: $$\displaystyle{A}={147.9}{e}^{{-{0.004}{t}}}$$

Exponential models

### The values of two functions, f and g, are given in a table. One, both, or neither of them may be exponential. Give the exponential models for those that are. $$\begin{array}{|l|l|}\hline x&-2&-1&0&1&2\\\hline f(x)&31.5&10.5&3.5&10.5&31.5\\\hline g(x)&0.2&0.6&1.8&5.4&10.8\\\hline\end{array}$$

Exponential models

### The values of two functions, f and g, are given in a table. One, both, or neither of them may be exponential. Give the exponential models for those that are. f(x)=? g(x)=? $$\begin{array}{|l|l|}\hline x&-2&-1&0&1&2\\\hline f(x)&1.125&2.25&4.5&9&18\\\hline g(x)&16&8&4&2&1\\\hline\end{array}$$

Exponential models

### When is the exponential population model appropriate? When is the logistic population model appropriate? When is an Allee model appropriate? Discuss the bene ts of each of these models and their drawbacks.

Exponential models

### Find the exponential model $$\displaystyle{y}={a}{e}^{{{b}{x}}}$$ that fits the points (0, 2) and (4, 3)

Exponential models

### The values of two functions, f and g, are given in a table. One, both, or neither of them may be exponential. Decide which, if any, are exponential, and give the exponential models for those that are. $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{x}&-{2}&-{1}&{0}&{1}&{2}\backslash{h}{l}\in{e}{f{{\left({x}\right)}}}&{0.3}&{0.9}&{2.7}&{8.1}&{24.3}\backslash{h}{l}\in{e}{g{{\left({x}\right)}}}&{3}&{1.5}&{0.75}&{0.375}&{0.1875}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$

Exponential models

### The exponential growth models, $$\displaystyle{A}={33.1}{e}^{{{0.009}{t}}}$$ (Canada) and $$\displaystyle{A}={28.2}{e}^{{{0.034}{t}}}$$ (Uganda) describe the population of the indicated country, A, in millions, t years after 2006. Use this information to determine whether the statement is true or false: "The models indicate that in 2013, Uganda’s population will exceed Canada’s". If the statement is false, make the necessary change(s) to produce a true statement.

Exponential models

### The initial value of car is $24,000. After one year the value of the car is$19,3550. What exponential dunction models the expected value of the car? Estimate the value of the car after 4 years.

Exponential models

### The table shows the mid-year populations an of China (in millions) from 2002 through 2008. Year Population, an ___________________________ 2002 1284.3 2003 1291.5 2004 1298.8 2005 1306.3 2006 1314.0 2007 1321.9 2008 1330.0 ___________________________ Use the exponential regression feature of a graphing utility to find a geometric sequence that models the data. Let n represent the year, with n=2 corresponding to 2002.

Exponential models

### The exponential models describe the population of the indicated country, A, in millions, t years after 2010. Use these models to solve, What was the population of Japan in 2010? India: $$\displaystyle{A}={1173.1}{e}^{{{0.008}{t}}}$$ Iraq: $$\displaystyle{A}={31.5}{e}^{{{0.019}{t}}}$$ Japan: $$\displaystyle{A}={127.3}{e}^{{-{0.006}{t}}}$$ Russia: $$\displaystyle{A}={141.9}{e}^{{-{0.005}{t}}}$$

Exponential models

### g is related to one of the parent functions Describe the sequence of transformations from f to g. g(x) = 1/2|x - 2| - 3

Exponential models

### The exponential growth models describe the population of the indicated country, A, in millions, t years after 2006.Uganda’s growth rate is approximately 3.8 times that of Canada’s.Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Canada: $$\displaystyle{A}={33.1}{e}^{{{0.009}{t}}}$$ Uganda: $$\displaystyle{A}={28.2}{e}^{{{0.0034}{t}}}$$

Exponential models

### The exponential models describe the population of the indicated country A, in millions, t years after 2006. Which country has the greatest growth rate? By what percentage is the population of that country increasing each year? Country: 1 $$\displaystyle{A}={127.8}{e}^{{{0.006}{t}}}$$ Country 2: $$\displaystyle{A}={1096.9}{e}^{{{0.018}{t}}}$$ Country 3: $$\displaystyle{A}={147.4}{e}^{{-{0.003}{t}}}$$ Country 4: $$\displaystyle{A}={25.6}{e}^{{{0.023}{t}}}$$

Exponential models

### The exponential models describe the population of the indicated country, A, in millions, t years after 2010. Use these models to solve, When will India’s population be 1377 million? India: $$\displaystyle{A}={1173.1}{e}^{{{0.008}{t}}}$$

Exponential models

### Determine whether the function given by the table is linear, exponential, or neither. If the function is linear, find a linear function that models the data. If it is exponential, find an exponential function that models the data. x f(x) -1 8/7 0 8 1 56 2 392

Exponential models

### Your uncle purchases a new car for $22,499. The value of the car decreases by 11% each year. Write the exponential equation that models the car's value after t years. Exponential models ANSWERED asked 2021-09-13 ### Joe wants to rent an apartment with an initial monthly rent of$1,400. He has been told that the landlord raises the rent 1.25% each year. Set up an exponential function that models this situation. Calculate the rent after 12 years. Round to the nearest dollar.

Exponential models