Question

In 1982, the number of Starbucks was 5 shops. It has exponentially grown by 21% yearly. Let t= the number of years since 1982. Find an equation for this growth and find the number of Starbucks predicted in 2015

Answer 1

The equation for the growth of the number of Starbucks is A = 5(1 + 0.21)^t and the predicted number of Starbucks in 2015 can be found by substituting t = 2015 - 1982 into the equation

Step-by-step explanation:

To find the equation for the growth of the number of Starbucks, we can use the formula for exponential growth: A = P(1 + r)^t, where A is the final amount, P is the initial amount, r is the growth rate, and t is the number of years. In this case, P = 5 (the initial number of Starbucks), and since the growth rate is 21% yearly, we can convert that to a decimal by dividing it by 100: r = 0.21.

So the equation for the growth of the number of Starbucks is A = 5(1 + 0.21)^t.

To find the number of Starbucks predicted in 2015, we substitute t = 2015 - 1982 into the equation: A = 5(1 + 0.21)^(2015 - 1982).

Answer 2

The number of Starbucks predicted in 2015 is 2697.

Step-by-step explanation:

There is an increment of 21% on yearly basis.

In 1982, the number of starbucks were 5.

In 1983, the number of starbucks will be
`5* (121)/(100)`.

In 1984, The number will become
`5*(121)/(100) *(121)/(100) = 5* ((121)/(100) )^(2)`.

In the year of X, the number of starbucks will be
`5*((121)/(100) )^(t)`, where t = X - 1982.

In 2015, t = 2015 - 1982 = 33.

The number of starbucks in 2015 is
`5*((121)/(100) )^(33) = 2697`.