Question bank: Exponential Function: Inputs and Outputs

A culture of bacteria grows exponentially according to the function y = 100 * (1.05)^t, where y is the number of bacteria after t hours. A laboratory needs to produce a certain amount of a substance that is produced by the bacteria. However, the substance is collected only when the number of bacteria is a power of 4. Since the laboratory has a collection window of only 24 hours, determine the ideal time to start the collection in order to obtain the largest possible amount of the substance, knowing that the start of the collection must be a multiple of 4 hours and the collection must last for a continuous period of time.

Pedro recently started a job as an administrative assistant in a technology company. He received a spreadsheet containing the number of sales of a certain product over 5 months, and he noticed that the sales rate of the product follows an exponential function, that is, , where x represents the month and y represents the product sales. Based on his investigation, Pedro found out that the product sold 200 units in the first month and 800 in the third month. Based on this information, solve:

Imagine you opened a savings account with an initial deposit of R$1000. This bank offers an exponential interest rate of 5% per month. After three months, how much money will you have in your savings account? Consider the exponential function , where x represents the number of months and y is the amount in Brazilian Reais in the savings account.

A certain population of bacteria grows according to the exponential function P(t) = 100 * 2^(t/3), where P(t) is the number of bacteria at time t, measured in hours, from the beginning of the observation. A laboratory conducts an experiment and observes that at time t = 6 hours, the population of bacteria reached a value of P(6) = 1000 bacteria. Based on this data: 1) Determine the number of bacteria initially present in the population. 2) Calculate the time t, in hours, when the population will reach 8000 bacteria. Justify your answers mathematically, showing the necessary steps for the solution of both parts of the question.

A population of bacteria is modeled by an exponential function, where the number of individuals (P) grows according to the function P(t) = P0 * e^(kt), where P0 is the initial population, and k is the growth or decay rate. In an experiment, it is observed that an initial population of 5000 bacteria increases to 8000 in a period of 10 hours. With this data, determine the growth rate k of the bacteria population and predict how many bacteria will be present after 24 hours, assuming the growth rate remains constant.