An exponential growth/decay word problem. If spraying of grasshoppers

Now, for 800kg/km^2 insecticide used, G_alive/G_initial = 0.6 .. (40% killed) .. (2)So, if we use (2) in (1), we get:0.6 = exp(-k.800) = exp(-800k)ln(0.6) = -800kk = ln(0.6)/800 = -0.00153Now, for 98% killed, G_alive/G_initial = 0.02 .. (3)So, from (3) and (2), we get:exp(-0.00153.insecticide used) = 0.02/0.6 =
  • #1
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Homework Statement


If spraying of grasshoppers with 800kg/km^2 of a certain insecticide will kill 40% of these insects, how much insecticide is needed to kill 98% of the grasshoppers?
(assume exponential relationship)

Homework Equations


[tex]\int[/tex]dP/dt=[tex]\int[/tex]kp
lnP=kt+c
e^(kt+c)=P

The Attempt at a Solution


I set up an equation relating the amount of insecticide to how many die (exp decay -k)
800kg/km^2=Po(e^-k(.4))
im unsure as where to go from here...or if I am even on the right path
 
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  • #2
insecticide is the input not the output.
So,

G_alive/G_intial = exp(-k.insecticide used)

when insecticide used = 0 then G_alive/G_initial = 1 .. (no G killed)
 

What is the meaning of an exponential growth/decay word problem?

An exponential growth/decay word problem is a type of mathematical problem that involves a quantity that either increases or decreases at a constant rate over time. It follows an exponential function, where the change in quantity is proportional to the current amount.

What is the difference between exponential growth and decay?

Exponential growth occurs when a quantity increases at a constant rate over time, while exponential decay occurs when a quantity decreases at a constant rate over time.

How is spraying of grasshoppers related to exponential growth/decay?

The spraying of grasshoppers can be related to exponential growth/decay if the population of grasshoppers either increases or decreases at a constant rate due to the spraying. This can be modeled using an exponential function.

How do you solve an exponential growth/decay word problem?

To solve an exponential growth/decay word problem, you would need to first identify the initial amount, the growth/decay rate, and the time period. Then, you can use the formula A = A0 * r^t, where A is the final amount, A0 is the initial amount, r is the growth/decay rate, and t is the time period. Plug in the values and solve for the final amount.

What are some real-life applications of exponential growth/decay word problems?

Exponential growth/decay word problems can be used to model various phenomena in real life, such as population growth, compound interest, radioactive decay, and the spread of diseases. It is a useful tool in predicting and understanding how a quantity changes over time.

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