Find The Equation

Question

A certain type of lily is growing in a pond in such a way that the number of plants is growing exponentially. The number of plants, N, in the bond at time t is modeled by the function N(t)=ab^t, where a and b are constants and is measured in months. The table shows two values of the function.

t       N(t)

0      150

1      450

What is the equation that can be used to find the number of plants in the pond at time t?

Answer 1

Hi Luke,

 

This problem is asking you to find numerical values for a and b by using the information contained in the table.

 

Let's write the equation N(t) when t = 0:

 

     N(0) = 150 = ab⁰

 

Anything raised to the zero-th power is just 1. So:

 

     150 = a.

 

Nice! We're halfway done.

 

Now let's write out N(1), keeping in mind that a = 150:

 

     N(1) = 450 = 150b¹

 

Solve for b:

 

     450/150 = b

 

     3 = b.

 

Now that we know what a and b are both equal to, we can write out the equation for N(t):

 

     N(t) = 150 · 3^t

 

Hope this helps!