Question bank: Exponential Function: Inputs and Outputs

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Question 1:

Hard

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.

Exponential Function: Inputs and Outputs

Theorical Question

Contextualized Question

Question 2:

Medium

João works at an investment company and wants to analyze the growth of an investment based on the compound interest formula, which is an exponential function. The formula A = P * (1 + r)^t is used to calculate the accumulated value (A) of the principal invested (P) over a certain period (t), with a monthly interest rate (r). João knows that the initial investment, the principal, is R$ 5,000.00 and the interest rate is 2% per month.

Exponential Function: Inputs and Outputs

Question 3:

Medium

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:

Exponential Function: Inputs and Outputs

Question 4:

Medium

Exponential Function: Inputs and Outputs

Question 5:

Easy

A population of bacteria is growing exponentially, doubling in size every 3 hours. At the initial moment, the population is 100 bacteria. Considering that time is represented in hours and the number of bacteria is an exponential function of time, determine the mathematical expression that describes the number of bacteria as a function of time. Then, calculate how many bacteria there will be after 9 hours.

Exponential Function: Inputs and Outputs

Multidisciplinary Question

IARA TIP

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