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:

i did it myself and i got 4.2 (b) hope its right

step-by-step explanation: