Dr. Silas studies a culture of bacteria under a microscope. The function b_1 (t)=500〖(1.6)〗^t represents the number of bacteria t hours after Dr. Silas begins her study. Is this an exponential growth or decay? Explain how you know.
What does the value 500 represent in this situation?
The number of bacteria in a second study is modeled by the function b_2 (t)=800〖(1.6)〗^t.
What is the growth rate, r, for this equation?
What does the difference of 500 and 800 mean between the two studies?

a) Remember that the y-intercept of a exponential function  is , so the only thing to do to find the y-intercept in our functions is evaluate it at t=0:

We can conclude that the y-intercept of our function is (0,50), and it represents the initial bacteria population in the sample.

b) To find if the function is growing or decaying, we are going to convert its decimal part to a fraction. Then, we will compare the numerator and the denominator of the fraction. If the numerator is grater than the denominator, the function is growing; if the opposite is true, the function is decaying.

Remember that to convert a decimal into a fraction we are going to add the denominator 1 to our decimal and then we'll multiply both of them by a power of ten for each number after the decimal point:

Now we can rewrite our exponential function:

Since the numerator is grater than the denominator, it is growing faster than the denominator; therefore the function is growing.

c) The only thing we need to do here is evaluate the function at t=5:

We can conclude that after 5 hours Dr. Silas began her study will be 268.9 bacteria in the sample.

Step-by-step explanation:

this story was prepared by jim

mccullaugh in los angeles and

al stewart in new york.

new york the colossal success of "top gun" appears to have dramatically altered madison avenue's

perception of corporate sponsorship

of home video projects.

the paramount home video re- lease, featuring a 60- second diet

pepsi spot, was by no means the

first prerecorded video to carry an advertiser's plug, but it was the

first major theatrical release to do so. in the aftermath of the title's

success, paramount is widely ex- pected to ink a similar deal for

"crocodile dundee" or "star trek

iv" or both.

corporate america's new attraccds push british

recording sales

to 19% gain

london fueled by the compact

disk boom, the value of u.k. manu- facturer shipments of recordings

rose 19% in the 12 -month period ended march 1987, according to the

british phonographic industry.

total value of u.k. shipments for

the period was $755 million for all

configurations. (all value figures

are based on an exchange rate of

$1.68 to the pound sterling.)

cd sales totaled 10.7 million units

worth $121.3 million- compared

with 3.7 million units worth $39.5

million in the prior 12 months -and

accounted for two -thirds of the

overall gain in trade value. at present growth rates, says the bpi, cd

sales for calendar 1987 will reach 20

(continued on page 79)

step-by-step explanation: