A city's population is 12,000 and grows at 2.6% rate. What will the population be after 25 years? A city's population is 230,000 and decreases at a 4.4% rate. What will the population be after 14 years?

Step-by-step explanation:

First question.

We would apply the formula for exponential growth which is expressed as

A = P(1 + r)^t

Where

A represents the population after t years.

t represents the number of years.

P represents the initial population.

r represents rate of growth.

From the information given,

P = 12000

r = 2.6% = 2.6/100 = 0.026

n = 25 years

Therefore,

A = 12000(1 + 0.026)^25

A = 12000(1.026)^25

A = 22796

Second question

The formula for exponential decay is

A = P(1 - r)^n

r = 4.4% = 0.044

n = 14 years

P = 230000

Therefore,

A = 230000(1 - 0.044)^14

A = 230000(0.956)^14

A = 122501

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!