# Exponential models questions and answers

Recent questions in Exponential models

### What does the quotient rule of exponents say?

Jonas Bautista 2022-12-23

### How to simplify ${\left({e}^{3}\right)}^{2}{e}^{2}$?

klepnin4wv 2022-12-18

### Euler's formula to show $\mathrm{cos}t=\frac{{e}^{it}+{e}^{-it}}{2}$?

Dayanara Nash 2022-11-27

### How can I find the roots of ${x}^{3}-3x+1$ using Cardano's formula?So far, I found that$x=\sqrt[3]{\frac{-1+\sqrt{-3}}{2}}+\sqrt[3]{\frac{-1-\sqrt{-3}}{2}}$$x=\sqrt[3]{\frac{-1+i\sqrt{3}}{2}}+\sqrt[3]{\frac{-1-i\sqrt{3}}{2}}$$x=\sqrt[3]{\frac{-1}{2}+\frac{i\sqrt{-3}}{2}}+\sqrt[3]{\frac{-1}{2}-\frac{i\sqrt{-3}}{2}}$I am now trying to express each cubic radicand in their exponential form.

Josiah Owens 2022-10-22

### The population of a southern city follows the exponential law. If the population doubled in size over 19 months and the current population is 40,000​, what will the population be 4 years from​now?

Destini Jones 2022-08-31

### Express the following fraction in simplest form using only positive exponents.$\frac{15h}{3\left(h^3\right)^2}$

Neil Wiley 2022-02-12

2022-01-24

### The table below gives values of the function f and g and different values of x. Whatis f(g (1))?  x 1 2 3 f(x) 3 -6 2 g(x) 2 7 1

Kelly Nelson 2021-12-17

### How to graph $y={3}^{-x}$

Ann Tice 2021-11-16

2021-10-25

Haven 2021-09-27

### For the following exercises, consider this scenario: For each year t, the population of a forest of trees is represented by the function $A\left(t\right)=115\left(1.025{\right)}^{t}$. In a neighboring forest, the population of the same type of tree is represented by the function $B\left(t\right)=82{\left(1.029\right)}^{t}$. (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?

Ava-May Nelson 2021-09-25

### 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: $A=129.3{e}^{0.001t}$ Country 2: $A=1096.9{e}^{0.011t}$ Country 3: $A=28.7{e}^{0.028t}$ Country 3: $A=147.9{e}^{-0.004t}$

slaggingV 2021-09-25

### 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. $\begin{array}{|llllll|}\hline x& -2& -1& 0& 1& 2\\ f\left(x\right)& 31.5& 10.5& 3.5& 10.5& 31.5\\ g\left(x\right)& 0.2& 0.6& 1.8& 5.4& 10.8\\ \hline\end{array}$

Marvin Mccormick 2021-09-25

### 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)=? $\begin{array}{|llllll|}\hline x& -2& -1& 0& 1& 2\\ f\left(x\right)& 1.125& 2.25& 4.5& 9& 18\\ g\left(x\right)& 16& 8& 4& 2& 1\\ \hline\end{array}$

texelaare 2021-09-23

### 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.

bobbie71G 2021-09-22

### India is currently one of the world’s fastest-growing countries. By 2040, the population of India will be larger than the population of China. by 2050, nearly one-third of the world’s population will live in these two countries alone. The exponential function $f\left(x\right)=574{\left(1.026\right)}^{x}$ models the population of India, f(x), in millions, x years after 1974. Find India’s population, to the nearest million, in the year 2055 as predicted by this function.

bobbie71G 2021-09-22

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

mattgondek4 2021-09-20

### 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. $\begin{array}{|cccccc|}\hline x& -2& -1& 0& 1& 2\\ f\left(x\right)& 0.3& 0.9& 2.7& 8.1& 24.3\\ g\left(x\right)& 3& 1.5& 0.75& 0.375& 0.1875\\ \hline\end{array}$

Efan Halliday 2021-09-20

### 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 1 0 2 1 4 2 6 3 10

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