Insect larvae grow incredibly quickly over the first several days of their lives. The length of one particular species increases exponentially at a rate of 25% each day. A scientist studying this species of larva measures one specimen to be 3 mm in length at the beginning of his observation period. The scientist will transfer the larvae to a new environment once the larvae are over 9.16 mm long.

Question

Maxine

Mathematics

3 March, 01:10

Insect larvae grow incredibly quickly over the first several days of their lives. The length of one particular species increases exponentially at a rate of 25% each day. A scientist studying this species of larva measures one specimen to be 3 mm in length at the beginning of his observation period. The scientist will transfer the larvae to a new environment once the larvae are over 9.16 mm long.

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Brody Lam · Answer 1

The exponent graph for this question would be:

an = 3mm (1.25) ^t

If the target length of the larvae is 9.16 mm, the time needed would be:

an = 3mm (1.25) ^t

9.16 mm = 3mm (1.25) ^t

3mm*3.053=3mm (1.25) ^t

1.25^t = 3.053

1.25^t = 1.25^5

t=5