Exponential Decay And The Number

The given statement is true because the decay rate of 3% per hour indicates that the substance is undergoing exponential decay. In exponential decay, the quantity decreases by a fixed percentage over a fixed interval of time. In this case, the substance is decaying at a constant rate of 3% per hour, which is characteristic of exponential decay.

The expression e3 ·e5 can be simplified by multiplying the exponents. Since the base is the same (e), we can add the exponents together to get e^8. Therefore, the correct answer is e^8.

The expression 3^0 represents the power of 3 raised to the exponent of 0. Any number raised to the power of 0 is equal to 1. Therefore, 3^0 is equal to 1.

An exponential decay function does not necessarily become smaller and smaller until it reaches 0. It approaches but never actually reaches 0. As the input values increase, the output values become smaller and smaller, but they never reach 0. Therefore, the statement is false.

If the function is represented by e raised to the power of -x, then it is a decay function. This is because as the value of x increases, the exponent becomes more negative, causing the function to approach zero. In other words, the function decreases or decays as x increases. Therefore, the given answer "true" is correct.

An exponential decay function is a function in which the base is greater than 1 and the exponent is negative. In the given options, y=3^(-x) fits this criteria as it has a base of 3 (greater than 1) and the exponent is negative (-x). This means that as x increases, the value of y decreases exponentially. On the other hand, y=3^x represents exponential growth as the exponent is positive. Therefore, y=3^(-x) is the correct answer for an exponential decay function.

When money is deposited in a bank account with an interest rate compounded annually, the amount of money in the account grows exponentially over time. In this case, Nadia deposited $500 with an interest rate of 10%, meaning that her money will increase by 10% each year. This increase is compounded annually, resulting in exponential growth of her account balance. Therefore, the statement that this is an example of exponential growth is true.

The correct answer is b,b),B. The model for this problem is y = 500 (1.10)x. This model represents the amount of money in Nadia's bank account after x years with an interest rate of 10% compounded annually. The initial amount of money is $500 (y = 500) and it grows exponentially over time with the factor (1.10) representing the 10% interest rate. Therefore, the correct answer is b,b),B which corresponds to the correct model equation.

not-available-via-ai

An exponential decay function does not always have -x as its power. The power in an exponential decay function is typically a negative value, but it can be any negative constant, not just -x. Therefore, the statement is false.

hint: to check if A is the correct answer

put 5 instead of t in the equation and check if the length is 201

The correct answer is "only 257 g would remain after 5 hours." This can be determined by calculating the decay of the substance over time. Since the substance decays at a rate of 3% per hour, after 1 hour, 97% of the substance would remain (300 g * 0.97 = 291 g). After 2 hours, 94% of the substance would remain (291 g * 0.97 = 282.27 g). After 3 hours, 91% of the substance would remain (282.27 g * 0.97 = 273.70 g). After 4 hours, 88% of the substance would remain (273.70 g * 0.97 = 265.89 g). Finally, after 5 hours, 85% of the substance would remain (265.89 g * 0.97 = 257.69 g), which rounds down to 257 g.

The correct answer is y=(0.25)^x. This equation represents an exponential decay function, where the base is less than 1. As x increases, the value of (0.25)^x decreases rapidly. This is reflected in the graph, where the y-values decrease exponentially as x increases. The other two equations, y=-(0.25)^x and y=(0.5)^x, do not accurately describe the graph as they either have a negative sign or a base greater than 1, which would result in exponential growth or different patterns.

An exponential function is a mathematical function in which the independent variable is in the exponent. In the given options, only the equation y=(1/3)^x fits this definition. The variable x is in the exponent, indicating that the function is exponential. The base of the function is 1/3, which means that as x increases, the value of y will decrease exponentially.

If a radioactive substance decays at a rate of 3% per hour, it means that after each hour, 97% of the substance remains. To find out how much time has passed, we can set up an equation:

200g * (0.97)^t = 147g

where t represents the number of hours that have passed. Solving this equation, we find that t is approximately 10 hours. Therefore, the correct answer is 10 hours.

The correct answer states that the answer to 21 is 3e^4. This means that when evaluating an expression or equation where the variable is equal to 21, the result will be 3 multiplied by e raised to the power of 4. The value of e is a mathematical constant approximately equal to 2.71828. Therefore, the answer to 21 is 3 multiplied by 2.71828 raised to the power of 4.

The length of the shark when it is 7 years old can be found by substituting t = 7 into the given function. By plugging in the value, we get l = 337 - 276e^(-0.178*7). Evaluating this expression, we find that the length is approximately 257.61 cm. Therefore, the correct answer is 257.61 cm.

The correct answer is "the answer to 19 is e^(3x) / 3". This means that when solving the equation or problem labeled as "19", the result should be e raised to the power of 3x, divided by 3.

The given table represents the values of y for different values of x in the equation y = (2/3)^x - 1. By substituting the given values of x (0, 1, 2) into the equation, we can calculate the corresponding values of y. The answer provided, y->0, -.33, -.56, represents the calculated values of y for x = 0, 1, 2 respectively.

not-available-via-ai

The given answer states that the answer to question #34 is .513.

The given correct answer is false. This is because the natural base e, which is approximately equal to 2.71828, is not a rational number. A rational number can be expressed as a fraction, but e cannot be written as a fraction. Therefore, it is a decimal number and not a fraction.