Courtney L.

asked • 09/08/18# EXPONENTIAL EQUATIONS & FUNCTIONS

1)A culture of bacteria doubles in weight approximately every 2.5 hours. The number of bacteria after t hours later can be approximated by 𝑁(𝑡) = 175(2.5)𝑡

a) How many bacteria would there be initially (𝑡 = 0)?

2)Solve for x.

a) 43−2𝑥 = 64 b) 25𝑥+1 = 53𝑥

b) Find 𝑁(4). What does this number tell you in terms of this problem?

## 1 Expert Answer

Jeffrey K. answered • 09/27/20

Together, we build an iron base in mathematics and physics

Courtney:

These growth problem always involve an exponent, i.e., a power of time, t.

The comment is correct, except that we also need a growth factor, k.

So, N = 175 x 2^{kt/2,5} . . . . . . . (1)

Since it doubles every 2.5 hours, we can write: 2N = 175 x 2.5^{k(t+2.5)/2.5} . . . . (2)

Divide (1) by (2): 2 = 2^((kt / 2.5) + k) - kt/2.5) . . . . subtract exponents

= 2^{k}

=> k =1

The rest I leave for you as an exercise.

So, our growth equation is: N(t) = 175 x 2^{t/2.5}

Initially, t = 0 => N(0) = 175 x 2^{0}

= 175

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Arturo O.

^{t/2.5}09/08/18