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3 years ago

Ebuka's monthly rent is

Mathematics

2 answers:

vagabundo [1.1K]3 years ago

7 0

Answer:

750(1.04)^t

Step-by-step explanation:

Looked it up on khan academy

seraphim [82]3 years ago

3 0

Answer:

$R(t)=750\cdot 1.04^t$

Step-by-step explanation:

Function Modeling

We need to find a function that models the total cost R(t) of Ebuka's rent if he pays it t weeks late.

We know that the normal rate for the rent is $750. Each week she will be charged by an additional 4%. Let's suppose she is 1 week late. The rent will be

$750+4\%\cdot 750=750+4/100\cdot 750=750+30=780$

Assuming the percent interest is computed on the previous value, if Ebuka is 2 weeks late, the payment should be

$810+4/100\cdot 810=842.4$

Since the new value is computed from the previous value, it's an exponential grow, and the rate of change is

$1+4/100=1.04$

Each week t Ebuka is late, the total payment is

$\boxed{R(t)=750\cdot 1.04^t}$

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Answer:

Step-by-step explanation:

We are given the matrix

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b) To find the eigenvalues of A, we find the roots of the characteristic polynomials. In this case they are $\lambda=4,3,-1$

c) To find the base associated to the eigenvalue lambda, we replace the value of lambda in the expression $A-\lambda I$ and solve the system $(A-\lambda I)x =0$ by finding a base for its solution space. We will show this process for one value of lambda and give the solution for the other cases.

Consider $\lambda = 4$ . We get the matrix

$\left[\begin{matrix}0&0&0 \\ 1&-1&0 \\-2&3&-5 \end{matrix}\right]$

The second line gives us the equation x-y =0. Which implies that x=y. The third line gives us the equation -2x+3y-5z=0. Since x=y, it becomes y-5z =0. This implies that y = 5z. So, combining this equations, the solution of the homogeneus system is given by

$(x,y,z) = (5z,5z,z) = z(5,5,1)$