A population of protozoa develops with a constant relative growth rate of 0.4142 per member per day. On day zero the population consists of five members. Find the population size after eight days. Step 1 Since the relative growth rate is 0.4142, then the differential equation that models this growth is dP dt

Given :

A population of protozoa develops with a constant relative growth rate of 0.4142 per member per day.

On day zero the population consists of five members.

Differential equation :

To Find :

The population size after eight days.

Solution :

Rate of growth , R = 0.4142 .

Now ,

Differential equation is :

For n = 0 .

So ,the relation is .

Putting n = 8 .

Hence , this is the required solution .

11 dance tickets were sold. ( approx )

Step-by-step explanation:

Let x represents the number of car wash tickets, y represents the number of silly string fight tickets and z represents number of dance tickets,

Total tickets = 380,

⇒ x + y + z = 380 (1),

The car wash tickets were $5 each, the silly string fight tickets were $3 each and the dance tickets were $10 each, also total cost is $1460,

⇒ 5x + 3y + 10z = 1460 (2)

Also, there are twice as many silly string tickets as car wash tickets,

⇒ y = 2x (3)

From equation (1) and (2),

x + 2x + z = 380 ⇒ 3x + z = 380 (4)

5x + 3(2x) + 10z = 1460 ⇒ 11x + 10z = 1460 (5)

For finding the value of z,

3 × equation (5) - 11 × equation (4),

We get,

30z - 11z = 4380 - 4180

19z = 200

z = 10.5263157895 ≈ 11

Hence, 11 dance tickets were sold.