Open In App

Exponential Growth Formula

Improve
Improve
Like Article
Like
Save
Share
Report

Exponential growth is a data pattern that illustrates an increase over time by using an exponential function to create a curve. For example, the number of blogs increased at a monthly rate of about 15% over one year. Another example can be the population of a town increasing at a rate of 12% continuously. 

Exponential Growth Formula

As the name suggests, such a formula that involves exponents is called an exponential formula. The most commonly used version of the exponential formula is:

y = a(1 + r)t

where the beginning value is a, the time is t, the end value is y, and the rate of change is r in decimal form.

Sample Problems

Problem 1. A $100 gift card is the first prize in a radio station contest. A name is announced once a day. If the person does not call within 15 minutes, the award will be increased by 2.5 percent the next day. If there are no winners after t days, write an equation to express the value of the gift card in dollars.

Solution:

The equation for exponential growth is y = a(1 + r)t.

We have, a = 100, r = 2.5% or 0.025

⇒ y = 100(1 + 0.025)t

y = 100(1.025)t

In the equation y = 100(1.025)t, y is the amount of the gift card and t is the number of days since the contest began.

Problem 2. Suppose that there is no winner after 10 days in the above problem. Find the value of the gift card.

Solution:

As per the above problem, y = 100(1.025)t.

Here, t = 10. Then,

y = 100(1.025)10

y = 128.01

The value of gift card in 10 days would be $128.01.

Problem 3. Since 2000, the cost of attending college has increased by 5% each year. Write an equation for the amount of tuition t years after 2000 if the tuition in 2000 was $10850.

Solution:

The equation for exponential growth is y = a(1 + r)t.

We have, a = $10850, r = 5% or 0.05

⇒ y = 10850(1 + 0.05)t

⇒ y = 10850(1.05)t

Problem 4. What would be the tuition fee in 2015 for the above problem?

Solution:

As per the above problem, y = 100(1.025)t.

Here, t = 2015 – 2000 = 15. Then,

y = 10850(1.05)15

⇒ y = $22459.50

Problem 5. In 2010, a gym sold 550 memberships. Subscriptions have climbed by 3% per year since then. For t years, write an equation to reflect the number of memberships sold.

Solution:

The equation for exponential growth is y = a(1 + r)t.

We have, a = 550, r = 3% or 0.03

⇒ y = 550(1 + 0.03)t

⇒ y = 550(1.03)t

In the equation y = 550(1.03)t, y is the number of subscriptions sold and t is the number of years.

Problem 6. Find the number of memberships sold by the gym in 2020 in the above formula.

Solution:

As per the above problem, y = 550(1.03)t.

Here, t = 2020 – 2010 = 10. Then,

y = 550(1.03)10

⇒ y = 740 (approx.)


Last Updated : 24 Jan, 2024
Like Article
Save Article
Previous
Next
Share your thoughts in the comments
Similar Reads