Hannah invested $4000 in a savings account that that earned 2% interest compounded quarterly. she determined that if she does not withdraw or deposit any more money, the value of the account at the end of 3 years will be $4244.83.what error did Hannah make in her calculations? what will her account balance be after 3 years

Her account balance after 3 years is $4,246.71

Step-by-step explanation:

In this question, we are tasked with calculating what Hannah's account balance will be after 3 years and the error she made in her calculations

Mathematically, to calculate the account balance after 3 years, we use the formula for the compound interest as follows.

Mathematically, the amount A earned on a compound interest is calculated as

A = P

where A is the account balance after the number of years which is what we want to know

P is the initial amount invested which is $4000

r is the interest rate which is 2%(2/100 = 0.02) according to the question

n is the number of times interest is compounded per year which is 4(quarterly means every 3 months)

t is the number of years which is 3

We plug the values into the question;

A = 4000(1 + 0.02/4)^(3)(4)

A = 4000(1+0.005)^12

A = 4000(1.005)^12

A = $4,246.71

P.S ; I do not see Hannah's calculation and as such I cannot spot where she made the error in her calculations

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

you are having disney spells!