Write a function [math]f[/math] which models the population of the city [math]t[/math] years after 2010.
What is the population of the city in 2017?
What will the population of the city be in 2020?
By what factor does the population grow between 2010 and 2020?
What about between 2020 and 2030?
[size=150]Assuming no other charges or payments are made, find the balance on the card, in dollars, after 1 year if interest is calculated:[br][/size][br]annually
[list][*]Option A: [math]2\frac{1}{4}\%[/math] interest applied each quarter[/*] [*]Option B: [math]3\%[/math] interest applied every 4 months[/*] [*]Option C: [math]4\frac{1}{2}\%[/math] interest applied twice each year[/*][/list][br]If they plan on no deposits and no withdrawals for 5 years, which option will give them the largest balance after 5 years? Use a mathematical model for each option to explain your choice.
Is Elena correct that these two situations both offer a 12% nominal annual interest rate?
Is Elena correct that the two situations pay the same amount of interest?
What is the monthly interest rate?
Write an expression for the account balance, in dollars, after one year.
What is the effective annual interest rate?
Write an expression for the account balance, in dollars, after [math]t[/math] years.
Select [b]all[/b] the expressions that represent the loan balance after two years if no payments are made.
[size=150]Here is a graph of the function [math]f[/math] given by [math]f\left(x\right)=100\cdot2^x[/math].[br][br][img]data:image/png;base64,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[/img][br][br]Suppose [math]g[/math] is the function given by [math]g\left(x\right)=50\cdot\left(1.5\right)^x[/math].[br][/size][br]Will the graph of [math]g[/math] meet the graph of [math]f[/math] for any positive value of [math]x[/math]? Explain how you know.[br]
[size=150]Suppose [math]m[/math] and [math]c[/math] each represent the position number of a letter in the alphabet, but [math]m[/math] represents the letters in the original message, and [math]c[/math] represents the letters in a secret code.[/size][br][br][size=100][size=150]The equation [math]c=m+7[/math] is used to encode a message.[/size][br][br]Write an equation that can be used to decode the secret code into the original message. [/size]
What does this code say: "AOPZ PZ AYPJRF!"?