What property is -23 x 1 = -23 (I need an answer like distributive property, zero product, additive inverse etc.)

Answer: A toad population is increasing by about 7.5% each year.

An event organizer finds each year's attendance for the past five years is about 4/5 of the previous year's attendance.

Step-by-step explanation:

On the highway, Kareem's car gets 38 mpg.

This can be modeled with a linear relationship between the miles and the gallons of fuel needed.

Shu Fang has $25.75 deducted from her checking account every month.

Here we know that each month a constant amount is deducted from her, this is not an exponential relation.

A toad population is increasing by about 7.5% each year.

If the population initially was an amount P, after one year the population is P*1.075, after two years the population is P*(1.075)^2 and so on, this can be modeled with an exponential function where the years variable, the function will have the general form:

Population(y) = P*(1.075)^y

An event organizer finds each year's attendance for the past five years is about 4/5 of the previous year's attendance.

If the first year the population is X, the year after the attendance will be (4/5)X, and the year after this process applies again, so you have a 4/5 of the previous attendance, the attendance now is (4/5)^2*X

This also can be modeled with an exponential function, of the shape:

Attendance (y) = X*(4/5)^y, where again, y means years.

The thing you may notice is that in this case the model only works for the lapse of 5 years that the event organizer said.

Answer: it take 5.448 years for the population to reach one million.

Step-by-step explanation:

The population of a city is modeled by the equation

P(t) = 256,114e0.25t

where t is measured in years.

For the population to reach 1000000, it means that

1000000 = 256114e0.25t

1000000/256114 = e0.25t

3.9045 = e0.25t

Taking ln of both sides of the equation, it becomes

Ln 3.9045 = Ln e0.25t

1.362 = 0.25t

t = 1.362/0.25

t = 5.448 years

Final answer:

The city's population is modeled by an exponential function and to find when the population will reach one million, we need to solve the equation for t by setting P(t) = 1,000,000. This requires dividing by the initial population, taking the natural logarithm, and then dividing by the growth rate (0.25). The result is the time in years it takes for the city's population to reach one million.

Explanation:

Calculation of Population Growth Time

The city's population growth is modeled by an exponential function, P(t) = 256,114e0.25t. Here, P(t) is the population at time t and 'e' is Euler's number, approximately equal to 2.71828. Your goal is to find when the population reaches one million.

To do this, set P(t) = 1,000,000 and solve for t:

1,000,000 = 256,114e0.25t

You would divide both sides by 256,114 and then take the natural logarithm to isolate t:

t = ln(1,000,000 / 256,114) / 0.25

Use a calculator to solve for 't'. This gives the time in years it takes for the city's population to reach one million people. It's a clear demonstration of how exponential growth operates: as the population increases, it takes less time to add a certain number of individuals.

Learn more about Exponential Population Growth here:

brainly.com/question/39279467

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