After depositing an initial amount of $10,000 in a savings account that earns 4% interest compounded continuously, a person continued to make deposits for a certain period of time and then started to make withdrawals from the account. The annual rate of deposits was given by 3000 - 500t dollars per year, t years from the time the account was opened. (Here, negative rates of deposits correspond to withdrawals.)(a) How many years did the person contribute to the account before starting to withdraw money from it?(b) Let P(t) denote the amount of money in the account, tyears after the initial deposit. Find an initial-value problem satisfied by P(t). (Assume that the deposits and withdrawals were made continuously.)
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
After depositing an initial amount of $10,000 in a savings account that earns 4% interest compounded continuously, a person continued to make deposits for a certain period of time and then started to make withdrawals from the account. The annual rate of deposits was given by 3000 - 500t dollars per year, t years from the time the account was opened. (Here, negative rates of deposits correspond to withdrawals.)
(a) How many years did the person contribute to the account before starting to withdraw money from it?
(b) Let P(t) denote the amount of money in the account, t
years after the initial deposit. Find an initial-value problem satisfied by P(t). (Assume that the deposits and withdrawals were made continuously.)
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