The population p of a bacteria culture is modeled by p=4300e^kt, where t is the time in hours. if the population of the culture was 5800 after 40 hours, how long does it take for the population to double?

93 h

Step-by-step explanation:

P = 4300eᵏᵗ

1. Calculate the value of k

lnP = ln4300 + kt

ln5800 = ln4300 + k(40 h)

8.666 = 8.366 + 40k h

8.666 - 8.366 = 40k h

0.299 = 40 k h

k= 0.299/40 h = 7.481 × 10⁻³ h⁻¹

2. Calculate the time for the population to double

2 × 4300 = 4300eᵏᵗ

2 = eᵏᵗ

ln2 = kt

t = ln2/k = ln2/(7.481 × 10⁻³ h⁻¹) = 93 h

It takes 93 h for the population to double.

The total cost of commodities = $61.82

Step-by-step explanation:

Sam visited the mall to purchase a shirt and a pair of shoes. The price of the shirt is $12.72. The price of the pair of shoes is $44.00.

The tax rate in the shop = 9%.

We have to find the total price Sam has to pay.

The total cost of the shirt and the pair of shoes =  12.72 + 44 = $56.72

Now there is tax of 9%.

So the cost becomes 1.09 times the initial value.

Hence the final price = 56.72

                                    = $61.82

The final price of shirt and shoes = $61.82