The number of bacteria in a culture is increasing according to the law of exponential growth. The initial population is 250 bacteria, and the population after 10 hours is double the population after 1 hour. How many bacteria will there be after 6 hours?

The number of bacteria in a culture is increasing according to the law of exponential growth. After 3 hours there are 100 bacteria, and after 5 hours there are 400 bacteria. How many bacteria will there be after 6 hours?

The populations P (in thousands) of Horry County, South Carolina, from 1980 through 2010 can be modeled by P = 20.6 + 85.5e^0.0360t where t represents the year, with t = 0 corresponding to 1980. According to the model, when will the population of Horry County reach 350,000?

Suppose that you are asked to prove the parallelogram-diagonal theorem. Write a paragraph that explains how you would proceed . (Do not write the two-column proof.)

A company uses a truck to deliver its products. To estimate costs, the manager models gas consumption by the function $G(x)=\frac{1}{250}\left(\frac{1,200}{x}+x\right)$ gal/mile, assuming that the truck is driven at a constant speed of x miles per hour, for $x \geq 5.$ The driver is paid $20 per hour to drive the truck 250 miles, and gasoline costs$4 per gallon. a. Find an expression for the total cost C(x) of the trip. b. At what rate is the cost C(x) changing with respect to x when the truck is driven at 40 miles per hour? Is the cost increasing or decreasing at that speed?

The number of bacteria in a culture is increasing according to the law of exponential growth. The initial population is 250 bacteria, and the population after 10 hours is double the population after 1 hour.

(c) After how many hours will the bacteria count be 10,000 ?

Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between the temperature of the object itself and the temperature of its surroundings (the ambient air temperature in most cases). Suppose that the ambient temperature is 70 F and that the rate constant is 0.05 (min)^(-1). Write a differential equation for the temperature of the object at any time. Note that the differential equation is the same whether the temperature of the object is above or below the ambient temperature.

These exercises use the population growth model. A culture starts with 8600 bacteria. After 1 hour the count is 10,000. (a) Find a function that models the number of bacteria n(t) after t hours. (b) Find the number of bacteria after 2 hours. (c) After how many hours will the number of bacteria double?

A population of 752,000 decreases 1.4% per year. What will be the population after 18 years?

The populations P (in thousands) of Tallahassee, Florida, from 2005 through 2010 can be modeled by P = 319.2e^kt where t represents the year, with t = 5 corresponding to 2005. In 2006, the population of Tallahassee was about 347,000. According to the model, during what year will the population reach 410,000?

The populations P (in thousands) of Tallahassee, Florida, from 2005 through 2010 can be modeled by P = 319.2e^kt, where t represents the year, with t = 5 corresponding to 2005. In 2006, the population of Tallahassee was about 347,000. Find the value of k Is the population increasing or decreasing? Explain.

determine the principal P that must be invested at rate r, compounded monthly, so that $500,000 will be available for retirement in t years. r = 5%, t = 10

Which of these landforms is characteristic of an area with karst topography? a. mountains b. canyons c. sinkholes d. drumlins

By what fraction must

$$\frac { 5 } { 3 }$$

be multiplied to get a product of 1?