Katydid population is modeled by
N(t) = 50 / 1+9e^ -.33t
where t is number ofyears and N(t) is population is thousands at time t.
when will katydid population reach 40,000?
post it.
See your12:15am post.
To find when the Katydid population will reach 40,000, we need to solve the equation N(t) = 40.
The given equation for the Katydid population is: N(t) = 50 / (1 + 9e^(-0.33t))
Substituting N(t) = 40, we get the equation: 40 = 50 / (1 + 9e^(-0.33t))
To find the value of t, we need to solve this equation.
Here's how we can do that step by step:
1. Multiply both sides of the equation by (1 + 9e^(-0.33t)) to remove the fraction:
40(1 + 9e^(-0.33t)) = 50
2. Distribute 40 to both terms inside the parentheses:
40 + 360e^(-0.33t) = 50
3. Subtract 40 from both sides of the equation:
360e^(-0.33t) = 10
4. Divide both sides of the equation by 360:
e^(-0.33t) = 10/360
e^(-0.33t) = 1/36
5. Take the natural logarithm (ln) of both sides of the equation to remove the exponential term:
ln(e^(-0.33t)) = ln(1/36)
-0.33t = ln(1/36)
6. Divide both sides of the equation by -0.33:
t = ln(1/36) / -0.33
Now, using a calculator, we can evaluate the right side of the equation to find the value of t:
t ≈ -2.605
Therefore, the Katydid population is estimated to reach 40,000 in approximately 2.605 years.