CentreShifter said:I'm trying to calculate maximum power. Once I computed power as a function of time I took its derivative and set it equal to zero. Now it need to solve for time and I can't seem to get it done. What I have is...
[tex]-1000e^{-500t}-2000e^{-1000t}=0[/tex]
My first inclination is to use ln, but ln(0) is undefined. Any tips?
A negative exponent is a way of representing fractions or decimals in exponential form. It is written as a number with a negative sign in front of it, such as -3. It indicates the number of times the base should be divided by itself when written in fractional form. For example, 2-3 can be rewritten as 1/(2*2*2), which equals 1/8.
To solve an equation with a negative exponent, you can use the rule that states a-n = 1/(an). This means that you can move the base with the negative exponent to the denominator and change the exponent to positive. Then, you can solve the equation as you normally would.
Yes, a negative exponent can be a whole number. This is because a whole number can be written as a fraction with a denominator of 1. For example, 3-2 can be rewritten as 1/(3*3), which equals 1/9.
Negative exponents result in fractions or decimals because they represent the inverse of a number. When a number is raised to a negative exponent, it is being divided by itself a certain number of times. This is equivalent to finding the reciprocal of the number, which will result in a fraction or decimal.
Solving equations with negative exponents can be useful in many fields, such as physics, chemistry, and finance. For example, in physics, negative exponents are used to represent exponential decay, which is the decrease in the amount of a substance over time. In finance, negative exponents are used to calculate compound interest, which is the interest earned on an initial investment over time.