Exponential function - practice problems
An exponential function has the form f(x) = a·b^x where b > 0 and b ≠ 1, with the variable in the exponent. When b > 1, the function represents exponential growth; when 0 < b < 1, it represents exponential decay. The natural exponential function f(x) = e^x, where e ≈ 2.718, is particularly important in calculus and natural phenomena. Exponential functions have constant percentage rates of change and never equal zero or change sign. Their graphs pass through the point (0, a) and have a horizontal asymptote on the x-axis. Applications include compound interest, population models, radioactive decay, and learning curves in psychology and education.Number of problems found: 185
- Simple interest pa
If a sum of money at a rate of simple interest, doubles in 8 years, then it will become 3 times in how many years? - Compound continuously
Find the balance in the account after 10 years. P= $1900; r= 6% Compound continuously. - The value
The value of the property decreases every year at the rate of 5%. If its present value is 411540 USD, what was its value three years ago? - Doubling every day
If you start with 1 euro on day 1 and double your money daily, how many days before you get at least 1 million? - A town 3
A town with 12,000 people has been growing at a rate of 2.5% per year. How many years ago was the population 8,000? - Population growth 2
The present population of the town is 200,000. Its population increases by 10% in the first year and 15% in the second year. Find the population of the town at the end of the two years. - The cost 15 The cost of a machine depreciates every year by 10% of its cost at the beginning of the year. If the present cost of the machine is USD 10000, find its cost after 2 years.
- The population 4
The population of a city is decreasing at a rate of 2% per year. The population in 2002 was 700,000. What would be the population in 2009? - Interest over time
If certain sum at compound interest becomes double in 5 years, then, in how many years, it will be 16 times at the same rate of interest? - An apple 2
An apple tree was planted two years ago. It increases at the rate of 20% every year .If at present, the height of the tree is 540 cm, what was it when the tree was planted? - Person A,B
Person A takes 3000 USD from person B for 2 yrs at the rate of 10% half yearly interest. What amount will be paid by person A to B after the end 2 yr? - A population
A population of fish starts at 8,000 and decreases by 6% per year. Use an exponential function to find the population of fish in 10 years. - The enrolment 2 The enrolment at a school has increased from 1400 learners to 1600 learners over 5 years. What is the percentage increase in enrolment?
- HCF of polynoms Find the HCF of the given expression: 2a²b²c4, 2a4b³c³ and 4a²b³
- Compound interest Joel borrowed $3208.5 on November 2, 2021, at 3.6% p.a. How many days would it take for him to repay the loan if he made a payment of $ 3,720.34? Round up to the nearest day.
- The sum 41 The sum of 640.00 was deposited in the first bank for five years, and the interest given was 160.00. Find the rate.
- Exp decay An element with a mass of 780 grams decays by 16.3% per minute. How much of the element is remaining after 16 minutes, to the nearest 10th of a gram?
- The balance 2 If your balance at the end of 4 years is 50000, at a 5% interest rate, What was your original investment?
- Flower series
Every day, the flower develops two new flowers, and each of these new blossoms also bears two flowers each day. After eight days, how many blooms are already present in the garden? - A company 2
A company invests 51000. After 4 years of growth at the same rate each year, the investment is worth 68920. Find the annual growth rate as a percentage.
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