mateo and his cousins are saving to purchase an avocado farm. they invest $25,000 in an account earning 8%…

mateo and his cousins are saving to purchase an avocado farm. they invest $25,000 in an account earning 8% interest each year. mateo thinks the equation below can be used to determine how much money, y, they will have in the account after investing for x years. is mateos equation correct? use the drop - down menus to explain.\n\n$y = 25,000(0.08)^x$\n\nclick the arrows to choose an answer from each menu.\n\nthe amount of money in the account after 1 year can be determined by evaluating the expression choose... . the amount of money, y, in the account after x years can be calculated using the equation choose... . mateos equation choose... correct.

mateo and his cousins are saving to purchase an avocado farm. they invest $25,000 in an account earning 8% interest each year. mateo thinks the equation below can be used to determine how much money, y, they will have in the account after investing for x years. is mateos equation correct? use the drop - down menus to explain.\n\n$y = 25,000(0.08)^x$\n\nclick the arrows to choose an answer from each menu.\n\nthe amount of money in the account after 1 year can be determined by evaluating the expression choose... . the amount of money, y, in the account after x years can be calculated using the equation choose... . mateos equation choose... correct.

Answer

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula for annual compounding is $y = P(1 + r)^x$, where $P$ is the principal amount, $r$ is the annual interest rate as a decimal, and $x$ is the number of years. Here, $P=$25000$ and $r = 0.08$.

Step2: Find the amount after 1 year

The amount of money in the account after 1 year is $y=25000(1 + 0.08)^1=25000\times1.08$.

Step3: Find the general formula for $x$ years

The amount of money $y$ in the account after $x$ years is $y = 25000(1 + 0.08)^x=25000(1.08)^x$.

Step4: Evaluate Mateo's equation

Mateo's equation $y = 25000(0.08)^x$ is incorrect because in the compound - interest formula, the base of the exponent should be $1 + r$ (the growth factor), not just $r$.

Answer:

The amount of money in the account after 1 year can be determined by evaluating the expression $25000\times1.08$. The amount of money, $y$, in the account after $x$ years can be calculated using the equation $y = 25000(1.08)^x$. Mateo's equation is not correct.