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- Solve inhomogenous ODEA bacteria culture is known to grow at a rate proportional to the amount present. After one hour, 1000 bacteria are observed in the culture; and after four hours, the population increased by 150%. Find an expression for the number of bacteria present in the culture at any time t.Find the second-order derivative of the function f(x) = log5 sin x + (2x2 - 8) / (x4 - 4x2). Please show complete solution.
- Use definition of hyperbolic function to prove that 2 sinh x cosh x = sinh 2x. Hence, solve the equation 8 sinh x = 3 sechx leaving your answer in terms of natural logarithms.A person invested $530 in an account growing at a rate allowing the money to double every 8 years. Write a function showing the amount of money in the account after t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year, to the nearest hundredth of a percentGive 1 problem for differentiation rule of exponential