Algebra Word Problem Solutions

Solve the given problem related to population growth.
During the first decade of this century the population of a certain city grew exponentially the population of the city was 146210 in 2000 and 217245 in 2010. Find the exponential growth function that models the population growth of the city use t= 0 to represent 2000 and t= 10 to represent 2010 and so on.
N(t)=?
Use your exponential growth function to predict the population of the city in 2016. Round to the nearest thousand.

Simplifying Expressions Involving Radicals Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.  ${\displaystyle \sqrt{x^5}{x}^5}$

Write an equation of the line that passes through the points.
(2, 5), (0, 5)

${\displaystyle 2+4^2(5-3)}$

Consider each set of numbers and determine if the set has an additive identity, additive inverse, multiplicative identity, or a multiplicative inverse. Explain your reasoning for each. a. the set of natural numbers.

Write in exponential form.
${\displaystyle \log 31=0}$

if a number is added three times to twice the reciprocal of the number.The answer is 5 .find the number

How do i round 56.479 cents to the nearest cent?

Here are the 2013 tuitions (in dollars) of 10 randomly selected 2 -year, public colleges (Source: U.S. Department of Education):
1772 1752 3485 1138 2328
1854 3598 3722 4680 3030​​
a. Find the mean tuition.

The recursive formula $A(n)=A(n-1)+5$ represents the amount of money in your savings account after n weeks. You start with $100. What is an explicit formula for the amount of money in your savings account after n weeks?
A. $A(n)=5+100(n-1)$
B. $A(n)=100(n-1)-5$
C. $A(n)=100+5(n-1)$
D. $A(n)=5(n-1)-100$

Anthony is working for an engineering company that is building a Ferris wheel to be used at county fairs. He wants to create an algebraic model that describes the height of a rider on the wheel in terms of time. He knows that the diameter of the wheel will be 90 feet and that the axle will be built to stand 55 feet off the ground. He also knows they plan to set the wheel to make one rotation every 60 seconds. Write at least two equations that model the height of a rider in terms of t, seconds on the ride, assuming that when t = 0, the rider is at his or her lowest possible height. Explain why both equations are accurate.
Part 2:One of Anthonys

Solve the equation and find the exact solution:
${\displaystyle \log base2\left(\log base3\left(\log base4\left(x\right)\right)\right)=0}$

Use Exponential Models in Applications
In the following exercises, solve.
Sayed deposits $20,000 in an investment account. What will be the value of his investment in 30 years if the investment is earning 7% per year and is compounded continuously?

Find the value of r so the line that passes through each pair of points has the given slope. (r, -5), (3, 13), m = 8

The Smiths spend 8% of their budget on entertainment. Their total budget this year is $2,000 more than last year, and this year they plan to spend $3,840 on entertainment. What was their total budget last year?

50 points decreased by 26%

Refer to right triangle ABC with $C={90}^{\circ }.$ Begin each problem by drawing a picture of the triangle with both the given and asked­for information labeled appropriately.
Also, write your answers for angles in decimal degrees.
If $a=42.3inchesandb=32.4$ inches, find B

Find the 37th term of an arithmetic sequence whose second and third terms are −4 and 12. If the fourth term of an arithmetic sequence is 17 and the second term is 3, find the 24th term.

Loretta, who turns eighty this year, has just learned about blood pressure problems in the elderly and is interested in how her blood pressure compares to those of her peers. Specifically, she is interested in her systolic blood pressure, which can be problematic among the elderly. She has uncovered an article in a scientific journal that reports that the mean systolic blood pressure measurement for women over seventy-five is 133.0 mmHg, with a standard deviation of 5.1 mmHg.
Assume that the article reported correct information. Complete the following statements about the distribution of systolic blood pressure measurements for women over seventy-five.
a) According to Chebyshev's theorem, at least $?36\mathrm{\%}56\mathrm{\%}75\mathrm{\%}84\mathrm{\%}or89\mathrm{\%}$ of the measurements lie between 122.8 mmHg and 143.2 mmHg.
b) According to Chebyshev's theorem, at least $8/9(about89\mathrm{\%})$ of the measurements lie between mmHg and mmHg. (Round your answer to 1 decimal place.)