PLEASE HELP!!!! The amount of money in alexander's account is y=4000-70x where y is the amount in dollars and x is the time in weeks.
a) determine the rate of change of money in alexander's account
b) find the x and y intercepts? interpret their meaning with respect to alexander's account
a. from the equation, rate of change is -70 dollars/week
b. x intercept, when y is zero, or x=4000/70
y intercept, when x is zero, 4000
y-intercept is the initial account balance (time=0)
x-intercept is how long it takes to empty the account (money=0)
a) The rate of change of money in Alexander's account is given by the derivative of the function y = 4000 - 70x with respect to x.
To find the derivative, we can differentiate the function term by term. The derivative of 4000 with respect to x is 0 since it is a constant. The derivative of -70x with respect to x is -70.
Therefore, the rate of change of money in Alexander's account is -70.
b) To find the x-intercept, we need to set y = 0 and solve for x.
0 = 4000 - 70x
To isolate x, we can subtract 4000 from both sides:
-4000 = -70x
Dividing both sides by -70, we get:
x = 4000/70
Simplifying, x ≈ 57.14
So, the x-intercept is approximately 57.14.
To find the y-intercept, we need to set x = 0 and solve for y.
y = 4000 - 70(0)
Simplifying, y = 4000
Therefore, the y-intercept is 4000.
The x-intercept represents the number of weeks it would take for Alexander's account balance to reach zero. In this case, it would take approximately 57.14 weeks for Alexander's account balance to reach zero.
The y-intercept represents the initial amount of money in Alexander's account. In this case, it is $4000, which means Alexander starts with $4000 in his account.