Acolony of bacteria is grown under ideal conditions in a laboratory so that the population increases exponentially with time. at the end of 3 hours, there are 10,000 bacteria. at the end of 5 hours, there are 40,000 bacteria. how many bacteria were present initially?

There were 1,250 bacteria present initially.

Step-by-step explanation:

To find the exponential growth to this, lets create an exponential model shown as below:

f(x) = a()

 Let y represent the amount of hours have passed after the third-hour recording. With the information given, we can create a set of input-output pairs: (0 , 10000) and (2 , 40000). Now that we have this set of pairs, we have given ourselves the initial value of the function, a = 10,000. We can now substitute the second point into the equation using N = 40,000.

N(y) = 10000b^y

40000 = 10000b^2    Divide and write in lowest terms.

÷10000   ÷10000

4 = b^2

b = Isolate b using properties of exponents.

b = 2

Now that we have the exponential growth, we can use b = 2 to work backwards and find the initial amount of bacteria.

10,000 ÷ 2 = 5,000 <-- Amount of bacteria 2nd hour

5,000 ÷ 2 = 2,500 <-- Amount of bacteria 1st hour

2,500 ÷ 2 = 1,250 <-- Initial amount of bacteria.

The initial amount of bacteria is 1,250

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

step-by-step explanation:

yes it represnts a functio, their are not 2 of the same numbers on the both sides