Suppose the rate of growth of bacteria in a petri dish is given by q(t)=12 t, where t is given in hours and q(t) is given in millions of bacteria per hour. if a culture starts with 89,000,000 bacteria, find a function q(t) that gives the number of bacteria in the petri dish at any time t. how many bacteria are in the dish after 3 hours

a) Q(t) = 89 + 12t

b) Q(3) = 125  millions of bacteria

Step-by-step explanation:

a)

to write a function of the growth of bacteria, we need to consider the initial population and add it to the new bacteria. Also we need to consider that the result of the function is in millions of bacteria, so when we get a result, we express it in millions.

Data

Initial population = 89 just add it to the function given   12t

          Q(t) = 89 + 12t

b) Data     time = 3 h

      Q(3) = 89 + 12(3)    substitution

      Q(3) = 89 + 36       simplifying

      Q(3) = 125 millions of bacteria

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18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²