Exponential equations are essentially mathematical formulas that incorporate exponents. These equations usually take the shape of a^x = b, where 'a' denotes the base, 'x' symbolizes the exponent, and 'b' signifies the outcome. These types of equations are commonly utilized in simulating growth or decay processes, the dynamics of population, as well as calculations related to finance among other uses.
| Topic | Problem | Solution |
|---|---|---|
| None | In 2004 , an art collector paid $\$ 84,053,000$ f… | The value of the painting is given by the function \(V(t)=30000 \times e^{0.147 t}\), where \(t\) i… |
| None | Find the half-life of a radioactive element, whic… | We are given the decay function of a radioactive element as \(A(t)=A_{0} e^{-0.022 t}\), where \(t\… |
| None | A radioactive substance decays according to the f… | We are given a radioactive substance that decays according to the function \(y=y_{0} e^{-0.019 t}\)… |
| None | The half-life of a certain tranquilizer in the bl… | We are given that the half-life of a certain tranquilizer in the bloodstream is 30 hours. This mean… |
| None | Suppose that the number of bacteria in a certain … | We are given a continuous exponential growth model, which is represented by the formula: \(P(t) = P… |
| None | Certain radioactive material decays in such a way… | The problem provides the function \(m(t)=370 e^{-0.045 t}\) which gives the mass remaining after \(… |
| None | A sample of $600 \mathrm{~g}$ of radioactive lead… | Given the function \(A(t)=600 e^{-0.032 t}\), where \(t\) is time in years and \(A(t)\) is the amou… |