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Nonamiya [84]
3 years ago
13

Enrollment in a dance studio has grown exponentially since the studio opened. A graph depicting this growth is shown. Determine

the percentage rate of growth.
0.25%
1.25%
2.5%
25%

Mathematics
1 answer:
denis23 [38]3 years ago
5 0

Answer:

Option (4). 25%

Step-by-step explanation:

The graph attached shows the exponential growth.

Let the graphed function is y = (1+\frac{r}{100})^{t}

Here 'r' = Rate of growth

t = Duration of time in years

y = enrollments after time 't' years

Graph shows at time 't' = 0 or initially number of enrollments = 20

After 8 years number of enrollments will be

120 = 20(1+\frac{r}{100})^{8}

\frac{120}{20}=(1+\frac{r}{100})^{8}

6 = (1+\frac{r}{100})^{8}

log 6 = 8\text{log}(1+\frac{r}{100})

0.77815 = 8\text{log}(1+\frac{r}{100})

\text{log}(1+\frac{r}{100}) = 0.0972689

(1+\frac{r}{100})=1.251

\frac{r}{100}=0.251

r = 25.1%

r ≈ 25%

Therefore, Option (4) will be the answer.

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