The population of Collin
County which follows the exponential growth model, increased from 491,675 in 2000 to 782341 in 2010?

(a) k=0.06217

(b)

(c) 556,755 is the population in 2012

Step-by-step explanation:

Population increased from 264,036 in 1990 to 491,675 in 2000.

Let assume , year 1990 as t=0

When t=0, population P = 264,036

When t=10, population P = 491,675

Exponential growth equation is P=P_0e^(kt)

is the initial population when t=0

So

When t=10, population P = 491,675

Plug in all the values and find out k

Divide both sides by 264036

To remove 'e' we take ln on both sides

The value of ln(e) = 1

Divide both sides by 10

k=0.06217

Exponential growth equation is

We know  

Replace the value of k

Now , we find the population in 2012

For year 2012 , t= 12

So we plug on 12 for t  and solve for P

P = 556755.09504

556,755 is the population in 2012

(a) k=0.06217

(b)

(c) 556,755 is the population in 2012

Step-by-step explanation:

Population increased from 264,036 in 1990 to 491,675 in 2000.

Let assume , year 1990 as t=0

When t=0, population P = 264,036

When t=10, population P = 491,675

Exponential growth equation is P=P_0e^(kt)

is the initial population when t=0

So

When t=10, population P = 491,675

Plug in all the values and find out k

Divide both sides by 264036

To remove 'e' we take ln on both sides

The value of ln(e) = 1

Divide both sides by 10

k=0.06217

Exponential growth equation is

We know  

Replace the value of k

Now , we find the population in 2012

For year 2012 , t= 12

So we plug on 12 for t  and solve for P

P = 556755.09504

556,755 is the population in 2012

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

The answer is in the image 

The answer is in the image 

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

The solution is given in the image below

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

The answer is in the image