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AURORKA [14]
4 years ago
14

The mass of a particular substance is known to grow exponentially at a rate of 1.5% per day. Its initial mass was 230 grams and,

after t days, it weighed 325 grams.
The equation modelling this growth is

230×1.015 t  =  325.

Use the method of taking logs to solve this equation for t, giving your answer correct to the nearest day.
Mathematics
1 answer:
Papessa [141]4 years ago
7 0

Answer:

23 days

Step-by-step explanation:

Given that the mass of a particular substance is known to grow exponentially at a rate of 1.5% per day

Initial mass = 230 gm

After t days, mass = 325 gm

The equation is

P(t) = 325 = 230 (1+\frac{1.5}{100} )^t\\\frac{325}{230} =1.015^t\\log 1.413 = t log 1.015\\t = \frac{log 1.413}{log 1.015} =\frac{0.1502}{0.0065} \\=23.229

Approximately after 23 days the mass will become 325 gms.

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