Question

In a Petri dish, there were initially 4 bacteria. Five hours later, there were 972 of them.

Find the exponential function that satisfies the given conditions.

f(t) = 4e^?*t

Answer 1

I don't know exactly what the question was, but I'm guessing it's the bacteria growth rate.

You can use the formula

final amount of bacteria = (initial amount of bacteria)(bacteria growth rate)^number of hours

So,

972 = (4)(x)^5

then simplify this equation to solve for x

x=3

the amount of bacteria increased 3 times more every hour for 5 hours

#copied

Answer 2

An exponential function has the form y = ab^x, where a and b are constants and x is the independent variable (in this case, time).

Given the initial condition that there were 4 bacteria in the dish, we know that when x = 0, y = 4.

So we can set up the equation: 4 = a(b^0)

Given the condition that 5 hours later there were 972 bacteria in the dish, we know that when x = 5, y = 972.

So we can set up the equation: 972 = ab^5

We can now solve for b by dividing the two equations:

972/4 = ab^5/a(b^0) = b^5

b = (972/4)^(1/5)

With b calculated, we can substitute it into one of the equations to find a:

4 = a(b^0) = ab^0 = a

So the exponential function that satisfies the given conditions is:

y = ab^x = 4(b^x) = 4( (972/4)^(1/5)^x)

This function models the growth of bacteria in the Petri dish