In 2000, a company had 1147 stores nationwide. By 2002, this total had grown to 1542. If the number of stores continues to grow exponentially at the same rate, how many stores will there be in 2016?

12226 stores will be there in 2016

Solution:

The growth function is given as:

Where,

y is the future value

a is the initial value

r is the growth rate

t is the number of years

From given,

In 2000, a company had 1147 stores nationwide

By 2002, this total had grown to 1542

Therefore,

y = 1542

a = 1147

t = 2000 to 2002 = 2 years

r = ?

Substituting we get,

Taking square root of both sides

If the number of stores continues to grow exponentially at the same rate, how many stores will there be in 2016?

Therefore,

y = ?

a = 1147

r = 0.1594

t = 2000 to 2016 = 16 years

Substituting we get,

Thus 12226 stores will be there in 2016

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages