Abacteria culture is started with 300 bacteria. after 4 hours, the population had grown to 500 bacteria. if the population grows exponentially. a: write a recursive formula for the number of bacteria. b: write an explicit formula for the number of bacteria. c: if this trend continues, how many bacteria will there be in 1 day?

a).

b).

c). 6429 bacteria

Step-by-step explanation:

Population of the bacteria grows exponentially.

Therefore, growth of the bacteria will be represented by the formula

Where = Population of the bacteria after time t

= Initial population of the bacteria

k = growth constant

t = time taken for growth

Now we plug in the values in the formula

= 500

= 300

Time t = 4 hours

Now we take the natural log (ln) on both the sides

4k(lne) = ln(500) - ln(300)

4k = 6.2146 - 5.7038

4k = 0.5108

k =

a). Recursive formula for the sequence formed by the bacterial growth

Since

500 = (1 + r)300

r =

Therefore, the recursive formula will be

b). Explicit formula for the number of the bacteria will be

c). We have to calculate the number of bacteria after 24 hours

bacteria

The x intercept is 5

Step-by-step explanation:

4x + 2y = 20

To solve for the x intercept, remove the y and solve for x:

4x = 20

x = 5

The x intercept is 5