When observations begin at $t=0$, a cell culture has $1200$ cells and continues to grow according to the function $p(t)=1200 e^t$, where $p$ is the number of cells and $t$ is measured in days. (a). Compute $p^{\prime}(t)$. What units are associated with the derivative and what does it measure? (b). On the interval $[0,4]$, when is the growth rate $p^{\prime}(t)$ the least? When is it the greatest?

The growth of Mycobacterium tuberculosis bacteria can be modeled by the function

$$N ( t ) = a e ^ { 0.166t },$$

where N is the number of cells after t hours and a is the number of cells when t = 0. a. At 1:00 P.M. there are 30 M. tuberculosis bacteria in a sample. Write a function that gives the number of bacteria after 1:00 P.M. b. Use a graphing calculator to graph the function in part(a). Describe how to find the number of cells in the sample at 3:45 P.M.

Suppose that $P' (t) = 0.15 P(t)$ represents a mathematical model for the growth of a certain cell culture, where $P(t)$ is the size of the culture (measured in millions of cells) at time $t$ (measured in hours). How fast is the culture growing at the time $t$ when the size of the culture reaches 2 million cells?

Solar photovoltaic (PY) cells are the world's fastest-growing energy source. In year t since 2007, PV cells were manufactured worldwide at a rate of $S=3.7 e^{0.61 t}$ gigawatts per year. Estimate the total solar energy-generating capacity of the PY cells manufactured between 2007 and 2011.

During an experiment, the number of ceils of a virus can be modeled by

$$P ( t ) = - 0.012 t ^ { 3 } - 0.24 t ^ { 2 } + 6.3 t + 8000$$

where t is the time in hours and P is the number of cells, jack wants to determine the times at which there are 8000 cells. Which values for t are reasonable and which are unreasonable? Explain.

Evaluate the following assertions about phototropism. Select True or False for each statement.

T/F Cells on the illuminated side of a stem elongate more than cells on the shaded side.
T/F Phototropism is triggered by blue light.
T/F Phototropins play a significant role in phototropism.
T/F The bending of the plant is due to cell elongation in response to auxin.

Let y(t) denote the number of E. coli cells in a container of nutrient solution t minutes after the start of an experiment. Assume that y(t) is modeled by the initial-value problem

$$\frac { d y } { d t } = ( \ln 2 ) 2 ^ { t / 20 }$$

, y(0)=20. Use this model to estimate the number of E. coli cells in the container 2 hours after the start of the experiment.

A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 60 cells. Find an expression for the number of cells after $t$ hours.

A cell of the bacterium $E$. coli divides into two cells every 20 minutes when placed in a nutrient culture. Let $y=y(t)$ be the number of cells that are present $t$ minutes after a single cell is placed in the culture. Assume that the growth of the bacteria is approximated by a continuous exponential growth model.

How long does it take for the number of cells to reach $1,000,000$ ?

A cell of the bacterium $E$. coli divides into two cells every 20 minutes when placed in a nutrient culture. Let $y=y(t)$ be the number of cells that are present $t$ minutes after a single cell is placed in the culture. Assume that the growth of the bacteria is approximated by a continuous exponential growth model.

How many cells are present after 2 hours?

Cells that inhibit T cell responses once a pathogen has been eradicated are called ._____

Lymphocytes that develop immunocompetence in the bone marrow are (a) T lymphocytes, (b) B lymphocytes, (c) NK cells, (d) B and T lymphocytes.

A cell of the bacterium E. coli divides into two cells every 20 minutes when placed in a nutrient culture. Let y=y(t) be the number of cells that are present t minutes after a single cell is placed in the culture. Assume that the growth of the bacteria is approximated by an exponential growth model. How long does it take for the number of cells to reach 1,000,000?

Jen, a biologist, is growing bacterial cultures at different temperatures as part of her research. The number of cells in the culture growing at 25 degrees C is given by the polynomial $t^2+4t+4$, where t is the time elapsed in minutes. The number of cells in the second culture growing at 35 degrees C is modeled by the polynomial $t^2+4$. She needs to measure the success of the 25 degree C culture over the 35 degree C culture. Find the polynomial representing how many more cells are in the 25 degree C culture for time t. How many more cells are there after 15 minutes?