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

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !

c 1 hour

step-by-step explanation:

m = 2e

m = 2 so 2 = 2e

1 = e