Question

im1 mini quiz 07: exponential fun...

1. the local rodent population numbers approximately 480 and is increasing at a rate of 8% per year.

2a write a function, y, that represents the population after t years.
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2b
increasing at a rate of 3% per year
write a function, y, that represents the population after
▶ $y = 750(1 + 0.03)^t$
▶ $y = 750(1.03)^t$
lets go back to the instructions
use the exponential growth formula $y = a(1 + r)^t$,
where
a is the original amount
r is the growth rate
t is time
here $a = 480$, $t = t$ and $r = 0.08$
your most recent input, $y(5) = 705.27744$, seems to be a calculation for the population after 5 years. however, the question is asking you to \write a function\ that represents the population after t years, not to calculate the population for a specific value of t.
lets take a step back and focus on creating the general function.
what is the formula for exponential growth? can you identify the initial population and the growth rate from the problem?
can i get a video, please?
can you explain why that was incorrect?

Explanation:

Step1: Recall exponential growth formula

The standard exponential growth function is $y = a(1+r)^t$, where $a$ is the initial amount, $r$ is the annual growth rate (in decimal), and $t$ is time in years.

Step2: Identify given values

We know $a = 480$, $r = 0.08$ (since 8% = $\frac{8}{100}$ = 0.08), and $t$ remains as the variable for time.

Step3: Substitute values into formula

Substitute the identified values into the growth formula.
$y = 480(1+0.08)^t$

Step4: Simplify the growth factor

Calculate $1+0.08$ to simplify the function.
$1+0.08 = 1.08$

Answer:

$y = 480(1.08)^t$