Exponential equation - practice problems
An exponential equation is one in which the variable appears in an exponent, typically in the form a^x = b or expressions involving exponential functions. Solving these equations often requires using logarithms to "bring down" the exponent, since logarithms are the inverse of exponentials. Common techniques include equating exponents when bases are the same, or applying natural logarithms to both sides. Exponential equations model rapid growth or decay processes including population growth, radioactive decay, compound interest, and epidemic spread. Solutions may involve properties of exponents and logarithms such as log(a^x) = x·log(a). Understanding these equations is crucial for science, finance, and modeling real-world phenomena involving exponential change.Remember: Solve each problem thoughtfully and make sure to show your complete solution for every question.
Number of problems found: 140
- 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? - GP - terms
Which term of the G.P., 2, 8, 32, ... up to n terms is 131072? - 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? - Of three
Of three positive numbers the product of the first and second is 42, second and third is 56 and that of third and first is 48. Find the third number. - A positive
A positive number plus itself squared is 240. What is the number? Please show your work. - 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? - Per annum
At a certain time, a sum becomes 4 times at the rate of 5% per annum. At what rate of simple interest the same sum becomes 8 times in the same duration - 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?
- 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?
- Years 3 How long will it take for a given sum of money to triple itself at 20% annual compound interest?
- A man 12
A man in his will shared his money geometrically among his six sons, so the eldest son received ; 5,589 and the youngest son received ; 736. (A)How much will the fourth son receive? (B)How much was shared among them - 56.9 divided
56.9 divided by 10 missing exponents = 0.569 - Chelsea Chelsea Donahue has a 20-year home mortgage of $74000 at 7.50% interest and will pay a $534 annual insurance premium. Her annual property tax will be $1534. Find her monthly PITI payment.
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