A bank account initially contains $25,000, and the account earns interest at a continuous rate of 7%

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Question:

A bank account initially contains $25,000, and the account earns interest at a continuous rate of 7% per year. (1) Write a differential equation for the balance in the account, B, in dollars, as a function of years, t. (2) Use the differential equation to calculate dB/dt at the start of year one (right after the money is deposited). State the units, and interpret your answers. Note: For the blank below, round your answer for part (2) to three decimal places. [Hint: This is an exponential (growth) model, and the interest rate is the proportionality constant. For part (2), derivative is the rate of change (earning the interest), which equals the right-hand side of the differential equation.]