Question

Exponential function is a function of the form:

a. y = a(1+r)^t
b. Ax + By = C
c. y = mx + b
d. y-y_1 = m(x – x_1)

Answer 1

The exponential function is of the form y = a(1+r)^t, representing situations where a quantity grows or decays at a rate proportional to its current size, used widely in fields like biology, finance, and statistics.

Step-by-step explanation:

The exponential function is a function of the form y = a(1+r)^t. It is a mathematical concept where the growth rate of a quantity is proportional to its current size, often used to model population growth, radioactive decay, and finance among other applications. In this formula, a represents the initial amount, r represents the rate of growth or decay, and t represents time. The function shows that as time progresses, the growth becomes more rapid if r is positive or declines more rapidly if r is negative, hence the term 'exponential'. This function can also help in the calculation of certain probabilities and distributions, such as the exponential distribution, which is often used to model the time between events in a Poisson process.