Please solve this differential equation problem. Provide step-by-step, well explained and readable.  Problem 1. (Exponential growth) Suppose a small colony of 1,000 bacteria, at t = 0 minutes is in a large bottle of water with lots of food and no predators (so there are no predation or density dependent issues to worry about). Suppose after 45 minutes there are 2,500 bacteria in the colony. Let y(t) = the number of bacteria in the colony at time t, t measured in minutes. Write the ODE IVP for the above scenario and find the solution to the IVP. Use the solution to estimate how many bacteria will be in the bottle at t = 90 minutes. Give your answer to the nearest thousandth (3 decimal places). Just put the number in the box, not the units.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.