Question

The number of bees in a colony was 25 in 1996 and has increased by 24% each year. Which exponential growth model shows the number of bees in the colony in terms of t, the number of years since 1996?options:y=25(24)t y=25(1.24)t y=25(0.24)t y=25+24t

Answer 1

Answer: $y\text{ = 25\lparen1.24\rparen}^t\text{ }$

Explanation:

Given:

The initial number of bees in the colony = 25

There is an increase = rate = 24% = 0.24

let the t = number of years since 1999

To find:

the exponential growth model in terms of t

To determine the growth model, we will use the formula for exponential growth:

$\begin{gathered} y\text{ = a\lparen1 + r\rparen}^t \\ where\text{ a = initial amount} \\ r\text{ -= rate of growth} \\ t\text{ = time} \end{gathered}$

substitute the values into the formula:

$\begin{gathered} y\text{ = 25\lparen1 + 0.24\rparen}^t \\ The\text{ function becomes:} \\ y\text{ = 25\lparen1.24\rparen}^t\text{ } \end{gathered}$